/mg/ - Math General

>>9098951
I remember using Pascal's triangle to answer a math question in high school. Got an A in that question too.

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Threadly reminder to work with physicists.

How do I get good at graphing equations? I'm prepping for the Oxford interview, and they often ask you to graph unusual functions and discuss their behavior.

Here are some example problems:
#1: Sketch y = 1/x^3 + x
#2: Sketch |y|^(1/2) = 1 - |x|^(1/2)

And then they might ask you to describe how the graph of #2 changes as the exponent varies (e.g. "what would it look like if it were 1/3 instead of 1/2?")

How do I get good at identifying the behavior of and being able to graph any function thrown at me?

Bonus: More specifically, how do I learn how to graph equations with operations on the y? What can I do that will make me be able to sketch something like tan(y) = x^2

Someone please help, I feel like theres a really simple answer but I can't figure it out and solving ugly polynomials doesn't seem feasible

Suppose I have a set of equations of the form

1/x1 + 1/x2 + ... 1/xn = f(m) * (1/(x1 + m*b) + 1/(x2 + m*b) ... 1/(xn + m*b))

For m in a set of integers (say, m = 1, 2, 3, 4, etc) and f(m) is some function that returns nonzero positive numbers, and b is some nonzero positive number.

How can I figure out how large n should be for this system to have solutions, and how can I see what they are? I feel really tempted to state that as long n is greater than the number of equations then it's all good, but these equations aren't linear so I can't use anything from lin alg to prove that.

Anything that could help?

>>9098958
Why are you posting this garbage here?

So did /mg/ ever come to a conclusion regarding applied mathematics?

>>9099023
I'm wondering as well.


I'm currently getting my PhD in applied mathematics, biology and physics.

So I would like to know more about various kinds of intuitions.

What is the best textbook for learning some Applied Mathematics?
I don't care about proofs so it's best if the textbook doesn't have them.

>>9099034
http://press.princeton.edu/titles/10592.html

>>9099023
last i checked there was a guy calling everyone redditors and saying that applied math doesnt exist

>>9098951

I have done method four in the course of my own problems to refresh my memory on multiple occasions. so quasi-ascended tier.

Pascal's triangle is no meme. It's useful as fuck, and useful to sketch out on-command without repairing to a calculator.

>>9098956
I'm in second year and I still use Pascale's triangle occasionally for small exponents

>>9098951
Now do Stirling numbers

>>9099470
do lah numbers

>>9098956
>Pascal's triangle instead of just applying the formula
Absolutely pleb tier

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>>9098960
>>9098960
the interviews are actually pretty good at being "unpreppable" ie more of an iq test.
but here are some things to think about:

with #2, we are graphing some equation of abs(x) and abs(y), so whatever it is, will be the same in each quadrant.

think in general about abs(x)^n + abs(x)^n = 1.
clearly (0,+1), (0,-1), (+1,0), (-1,0) will always be solutions
for n=2, we have a unit circle
for n=1, we have a "diamond-orientated" square

now think: intuitively as we went from n=2 to n=1, we "squeezed" the corners inwards (keeping the four points fixed). so as n gets smaller again, we do the same.

for larger n, we do the opposite (pull the corners out), till we end up with a unit square (which happens to be Max(abs(x),abs(y))=1).

the other q: consider tan(y)=x (this is just y=tan(x) with the coordinates switched).

tan(y)=abs(x) is the above with the right-hand side of the plane copy and pasted onto the left-hand side (because tan(y)=abs(-x) iff tan(y)=abs(x) ).
tan(y)=x^2 is the above with the graph "smoothed out" because x^2 is the "smooth version" of abs(x).

pic related

but if you want some advice from a 2nd year ox maths student who had shit grades -- FOCUS ON THE MAT. they just use the interview to check you arent somehow retarded.

good luck tho :) what college you thinking of?

>>9098979
>1/x1 + 1/x2 + ... 1/xn = f(m) * (1/(x1 + m*b) + 1/(x2 + m*b) ... 1/(xn + m*b))

btw, are x1 and x2 distinct variables or x^1 and x^2 ?

>>9099892
Wow, thanks for the input. That's very helpful.

What did you get on the MAT? How do you think your interview went? Did you ask for feedback?

I'm applying to SJC, which college are you at?

>>9100134
I did v well on the day
But I did all the past papers (about a dozen) available and got strictly increasing scores from below 40 to above 80 (i graphed it out somewhere) - so preparation is literally the most important thing desu.

I won't say the college bc there's only like six of us lmao. But I will confess I only so Maths and Philosophy not straight maths.

>>9099907
Distinct variables. I'm thinking about just going into some numerics.

>>9100134
oh and i never asked for feedback but my tutor might still have it on the system so might ask him.

id probs do each past paper twice actually (unless you are getting consistently very very high first time). value per effort the mat is far more important than a levels

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>>9098958
Which book is this from?

>>9100155
>I won't say the college bc there's only like six of us lmao
Smart idea, I wouldn't want to expose myself to the normies either.

>I did v well on the day
Which section was hardest for you, if you remember? I've done tests A, B, and 2007 so far, (getting ~49, ~55, 60 on each) and I always get 3 marks max on #4 (the geometry questions). My gap in geometry knowledge is so large that I don't even know where to start in order to improve. Do you have any tips for that, or is it just a matter of needing to git gud?

>>9100179
https://www.amazon.com/Quantum-Fields-Strings-Course-Mathematicians/dp/0821820125

>>9098951
Why even use math when you have physical intuitions?

>>9098960
>I'm prepping for the Oxford interview,
Underage B&

>>9100195
Tbf I am a normie. Otherwise I'd've gone Cambridge.
I never had to do geometry lmao but suspect just practice. Look at the tricks and just memorise them. Pray that the plasticity of a young brain will just retain the techniques. Maybe just brush up on basic geometry - but they won't use anything that EXPLICITLY uses more than c2

>>9100357
you are in your senior year of high school when at the age of 18

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>>9098951

> using the hypergeometric series instead

>>9099227
good to hear

>>9100409
The interviews are this December usually. The earliest birthday (unless they skipped a year somehow) would be September the 1st 2017 for this year's year 13 students.

[math]\mathcal{P}(\mathbb{R})[/math]

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>>9101268

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>>9101268
>>9101271

>>9101268
>>9101271
>>9101311
"Lol" as we physicists say.
I just solved this using my physical intuitions.

>>9101271
Right and wrong. Those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.

>>9101332
Assuming anything that is not proven (except axioms lol) cannot yield a proof. Any mathematician thinking otherwise is an idiot.

in case of integration of functions of multiple real variables, does the riemann way allow the integration of function that cannot be integrated in lebesgue theory

>>9101374
Riemann implies Lebesgue.

>>9101378
and is there a relevant improper riemann integration in multiple variables

>>9101390
Just use the same idea you would use for an inproper integral in only one variable, I guess. I'm not an analyst, sorry.
>does the riemann way allow the integration of function that cannot be integrated in lebesgue theory
I was just pointing out that this is the other way around, all Riemann integrable functions are Lebesgue integrable.

>>9101378
>>9101390
>>9101405
>Riemann
Assuming anything without proof can only be used to prove that it is wrong.

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I know this isn't a homework thread or something, but I came across a problem in my text book I can't seem to figure out. I'd appreciate it if someone could help me out (I don't want people to solve it for me, I really do want an explanation that would help me understand):
Let G = (V, E) be a graph with n nodes, such that the degree of each node is at most d. Prove that there exists in G a set S of independent nodes (meaning, a set that contains no adjacent nodes) so that |S| >= n/(d+1).
I tried proving by induction, but it requires me to split the problem into 3 different cases, and I can only prove it for 2 of them. (the 1st case is when you add a node that doesn't connect with any other node in G, the 2nd is when you add a node that connects with other nodes in G but not nodes in S, and the 3rd which I can't prove is when you add a node that connects with other nodes in G including ones in S).
Any help would be appreciated!

What is the current state of anabelian alebraic geometry

>>9098951
/brainlet/ here. A while ago i fantasized about using traveling waves to represent organisms traveling over evolutionary time. more specifically the waves would represent both genetic and epigenitic codes and they would travel over a gradient that represents the physical landscape, this and the waves interactions would effect the wave function. My idea is too use this to simulate ecological succession, population dynamics, disturbance scenarios, and evolution, it would be applicable in agroecology, conservation, and what not.
the problem is i didnt even pass algebra 2 and can pretty much only fantasize about it, assuming i caught up on math or got help, would this be a good start?
https://faculty.washington.edu/eeholmes/Files/Holmesetal1994.pdf
what are your thoughts?

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Why does G have to be commutative?

>>9101517
the waves would split with reproduction to show phylogeny, the interactions would be represented as signs from a biosemiotic perspective allowing to show them as networks of interactions.

>>9101527
>show them as networks of interactions.
that effect the dynamics of traveling waves.

>>9101522
My applied physical intuition says it should be commutative.

>>9101441
It's actually pretty good according to my physical intuition.

Prove that abelian groups exist.

>>9101680
Take the integers with addition

>>9101685
Show that the integers exist.

>>9101522
just consider the group S3 and let n = 3

>physical intuition
What's this meme?

>>9101428
Two thoughts, although I can offer no solution:

1. You usually cannot directly induct by taking one node and adding nodes and vertices. That would require proving that it is actually possible to obtain a Graph with n nodes that satisfies the assumptions in such a way, often not feasible.
Instead, you can take an arbitrary Graph satisfying the assumptions with n nodes, then remove any node such that the assumptions still hold and use the induction hypothesis on the resulting n-1-sized Graph.

2. Inducting as per above, if you remove a node [math]v[/math] and [math]S[/math] on the subgraph [math]G'[/math] with [math]n-1[/math] nodes has cardinality [math]|S| > \frac{n-1}{d+1}[/math], there is nothing to show.
If however [math]|S| = \frac{n-1}{d+1}[/math], you will need to show that [math]v[/math] can be added to [math]S[/math].
Clearly though, this is only the case if [math]N(v) \cap S = \varnothing[/math].
Therefore, you would need to show that [math]N(v) \cap S \neq \varnothing \Rightarrow |S| > \frac{n-1}{d+1}[/math].

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which godel proof is this?

>>9102098
dunno
what axiom did godel use to prove that there are no proofs without axioms?

>>9102098
It is true that deductive proof requires axioms.

But there are other forms of proof such as induction. These don't give you 100% certainty but in reality nor does deduction.

Peterson has admitted he can't math and he should stick to his knitting.

>>9102098
That is such a retarded statement. Man, I used to respect this guy when he first went viral but then I found out he was a christcuck and it all went to shit. He is clearly an intelligent person but his christianity has corroded his brain to the point that he will make this nonsensical statement just to justify his own christcuckism.

It is true that proof itself without axioms is impossible because to have a proof then you must have a statement that you want to prove, and if you have a statement then you have an underlying theory of which it is a statement of, and that underlying theory is a set of axioms. But to then conclude from this that god is a prerequisite for all proof is retarded because he is basically saying that axioms come from god which is retarded because historically we have been fiddling about with axiomatic systems, even to this day. So unless he is saying that mathematicians are gods then he is retarded.

>>9098951
Books to study set theory and logic?

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>>9102199
Anything from https://en.wikipedia.org/wiki/Saharon_Shelah

>>9096922


i am the OP of this thread asking for help and links i am curious where i can go from here. books on working problems like these? i guess the next step is the quartic.

>ax^3 + bx^2 + cx + d = 0
>t^3 + pt + q = 0
>(u+v)^3 + p(u+v) + q = 0
>(u+v)^3 = -q ; w^3 + wbar^3 = -q
>uv = -p/3 ;; 3wwbar = -p

depress the cubic into an associated quadratic via substitutions of the "complete the cube" flavor.

repeat, condense z^6 into (z^3)^2 and solve with substitutions of the "complete the square" flavor (quadratic equation).

but how do we get the values that satisfy these conditions?

im curious: when do they teach solving cubics in this manner?

i took calc over two years ago and i stumbled upon this problem while brushing up on my algebra a few days ago and have been working it since i encountered it.

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Fun question

(may require some knowledge of elementary number theory [https://en.wikipedia.org/wiki/Pell's_equation], but there may be a solution that works around that)

>>9102585

this can be 1

>>9102680
>this can be 1
There's no 1st Avenue.

Suppose an odd number n is defined by:
n = 2x + 1
Does the following prove that if n is odd, then n^2 is odd?
n^2 = (2x+1)^2
= 4x^2 + 2x + 2x + 1
= 4x^2 + 4x + 1
= 2(2x^2 + 2x) + 1
which falls into the definition of an odd number, 2x + 1.

I'm working in a discrete math book, trying to practise proofing, and in this example problem the book concluded that a direct proof wasn't really a good option, even though the proof i wrote up there seemed easy enough, and now I'm self-doubting myself. Is there anything wrong with the reasoning?

>>9102773
Any odd number times any other odd number gives an odd number, that's trivial

>>9102773
If you are looking to prove this statement, then >>9102798 is the right way to go.

Prove using modular arithmetic (mod 2) for a 1 line proof.

>>9102098
Analytic propositions don't require axioms...

>>9102705

ya sure and

>imaginary numbers arent real
>0 is infinity
>there is no 1st avenue

>>9102141
>But there are other forms of proof such as induction.
The principle of induction itself can't be proved without a much stronger principle.

I'm trying to prove that given an absolute value [math] |\cdot | [/math] (non-negative, multiplicative, satisfies triangle inequality) on a field [math] F [/math] that [math] |n|\leq 1 [/math] for all [math] n\in \mathbb{Z} [/math] implies [math]|\cdot | [/math] is non-archimedian (i.e. [math]|x+y|\leq max(|x|,|y|) [/math] for all [math] x,y\in F[/math]).

So far the best I can do is:

Assume [math] |n|\leq 1 [/math] for all [math] n\in \mathbb{Z} [/math]:
[eqn]
|x+y|^n =|(x+y)^n|\\
= |\sum_{i=0}^n \binom{n}{i} x^iy^{n-i}|\\
\leq \sum_{i=0}^n |\binom{n}{i} x^iy^{n-i}| \\
= \sum_{i=0}^n |\binom{n}{i}| |x|^i|y|^{n-i} \\
\leq \sum_{i=0}^n |\binom{n}{i}| max(|x|^n,|y|^n) \\
\leq \sum_{i=0}^n max(|x|^n,|y|^n) \\
= (n+1) max(|x|^n,|y|^n) \\
= (n+1) max(|x|,|y|)^n \\
[/eqn]

where the first inequality uses the triangle inequality, the second inequality is straightforward, and the third inequality uses the given assumption. How do I do better than the (n+1) factor?

>>9103259
An alternative direction (probably more of a wrong direction since it doesn't even use the hypothesis) is:

[eqn]
|x+y|^n \leq (|x|+|y|)^n\\
= \sum_{i=0}^n \binom{n}{i} |x|^i|y|^{n-i}
\\ \leq \sum_{i=0}^n \binom{n}{i} max(|x|,|y|)^n\\
=2^nmax(|x|,|y|)^n \\
[/eqn]

which implies [math] |x+y| \leq 2max(|x|,|y|) [/math]

Is there an expression equivalent to arccos((a*cos(x) + f)/(a + f*cos(x))) which does not use an inverse trig function or infinite series? Where a and f are constants and a > f > 0.

What is the physical intuition for the axiom of infinity?

>>9101685
I don't see a proof of this group supposedly being "abelian" in your post.

>>9103358
My physical intuition tells me "maybe".

>>9103358

arccos((a*cos(x) + f)/(a + f*cos(x))) =

π/2 + i log((i (f + 1/2 a (e^(-i x) + e^(i x))))/(a + 1/2 f (e^(-i x) + e^(i x))) + sqrt(1 - (f + 1/2 a (e^(-i x) + e^(i x)))^2/(a + 1/2 f (e^(-i x) + e^(i x)))^2))

What is the last "how to self-learn math" pasta nowadays? I want to brush up calc 1 and Linear algebra and go from there.

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>>9103608

>>9103615

Nice meme.

>>9103615
>>9103619
>>9103623
I agree! My physical intuitions actually told me this :D

I've spent the whole summer up to this point doing gen eds and have barely had anytime to do math. How screwed am I for this upcoming semester? It's only Calc III and an intro proof course so it's not too tough but I am a brainlet.

>>9103653
Try gaining some additional physical intuition for the math and you'll be fine. That's what I usually do lol
I don't even read any "books".

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>>9102199
http://www.logicmatters.net/2017/01/01/teach-yourself-logic-2017
>>9102805
>Analytic propositions

Why does Stone's theorem require the one-parameter group to be strongly continuous? What if I only have the weak operator topology?

>>9102142
lol way to throw the baby out with the bathwater. You do realize you don't have to agree with everything someone says in order to get useful value out of them right? Stop being so 1 dimensional

>>9102805
>Analytic propositions don't require axioms...
Example?

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At what point can an autodidact pick up an "Advanced Calculus" text, or even an "Analysis" text?

I've been working through Keisler's "Elementary Calculus" and have just finished learning about Integrals. I own a copy of an Advanced Calculus text. Looking through the TOC, there's quite a bit of overlap between that text and introductory calculus texts. Pic is a page from the TOC of the book in question.

I also recently picked up a copy of Apostol's "Mathematical Analysis" at an estate sale, which also seems very accessible.

I already have a foundation in logic, set theory, algebra, and trig, in addition to the calc I've already learned. Can I just dive into the "Advanced Calculus" or even "Mathematical Analysis" texts at this point?

>>9103790
I would encourage you to finish a computational calculus book before trying to proceed to those other two books. It will build the necessary background and mathematical maturity. I honestly might advise you to use a different book than Keisler's, he takes a pretty non-standard approach, the books by Stewart and Kline would be more traditional.

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>>9103615

>women's studies

Apex jej; the highest level of jej.

on behalf of the images' author, take my studious approval.

>>9103778
That there is at least one knowable truth. This proposition is analytic and doesn't require axioms because the truth-value of this proposition can be evaluated by means of logic; assuming the contrary would obviously be a contradiction

>>9098960
>>9099892
#2 is a second-degree polynomial in [math]t := x^{1/2}[/math]
you can just graph [math]y = 1 - 2t + t^2[/math], then rescale the [math]t[/math] axis to [math]x^{1/2}[/math], then just copy/paste in every quadrant to account for the absolute values

test

[eqn]\begin{bmatrix}f & u \\c & k \end{bmatrix}

x^{2} [/eqn]

>>9098956
I learned how to draw the analogues to Pascal's Triangle in up to 9 dimensions. I'm probably going to write a computer program to do it soon.

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>>9098951
you forgot to add that statlets are not welcome

>>9104532
This chart is the proof that none of you posting in the thread are true mathematicians or you're all fucking 1st year undergrads
Honestly these threads are all about basic calculus, retarded high school level questions and people who don't know what the fuck they're talking about

T. vertex algebras postdoc researcher

>>9104532
Good idea: trick all the shitters into avoiding the fields most helpful in getting a job.

>>9104532
>economics
>shit tier
Have fun being poor

How can some people make huge calculations in their own heads in a matter of seconds? Is it an innate ability or can it be learned? I find it quite fascinating that most genius or high level mathematicians could do that. There's even a program in China if I'm not mistaken about it, where ordinary kids make huge calculations in a very short amount of time.

>>9104622
Here's the program I'm talking about:

https://www.youtube.com/watch?v=FvhNnwrGBBs

Those fuckers are insane, how can one learn to calculate like that?

>>9104448
Ooh, that's clever. What class do you learn that approach in?

>>9104628
There's no way this is real.

>>9105158
it's just looking at the problem and not trying to box it into some sort of formulaic problem-solving approach. there's no class that can teach you to be clever or notice patterns, it comes down to experience and IQ at that point

t. mathfag

>>9105248
>not trying to box it into some sort of formulaic problem-solving approach.
>notice patterns

What do you mean by those? Can you give some examples?

>>9101428
It's simply pigeonhole principle.

Each vertex has at most d neighbors, together with the vertex they build a set of at most d+1 vertices.

Now consider the vertex set V. Select a vertex and put it in S, remove it and its neighbors. Repeat until there are no vertices left.

How many times can you select a vertex for S? At least ceiling (n/(d+1)) times.

This means that every independent set that can't be increased has at least this amount of vertices, especially the maximal independent sets.

>>9102585
If the house number is h and the avenue n then
[math]s = 1 + 2 + \dots + h = h + (h+1) + \dots + n[/math] so

[math]2s = 2h(h+1)/2 = n(n+1)/2 + h[/math]
[math]h^2 = n(n+1)/2[/math]
Solution for part 1 is n=8, h=6.

>>9104321
the word obviously is reserved for when a result clearly follows if the reader understood the text before.
you seem to use the word obvious in a broader context.

>>9104532
>neglecting to mention tensor analysis

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>>9105575
Good work

>>9104573
Most economics that isn't better grouped under either political philosophy or ecology is absolute shot

About to graduate with a BS in math, probably gonna get a master's.

Thinking about going to Europe for it. Where should I go?

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Best online resources for reviewing trig/precalc shit?

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lads, im taking an intro stats class. its okay so far, but i never did well in HS math (that was 5 years ago anyway), so i'm having trouble with fractions

can someone break down how he got 1/3 from that?

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>>9105792
Using physical intuition, [math]\frac{\frac{2}{36}}{\frac{6}{36}} = \frac{2}{36} \cdot \frac{36}{6} = \frac{2 \cdot 36}{6 \cdot 36} = \frac{2}{6} = \frac{1}{3}[/math]

>>9105792
You're dividing 2/36 by 6/36. So it goes: (2/6)x(36/6). The 36s cancel out and you're left with 2/6=1/3.

>>9105792
This is baby's level mathematics, you should be able to do that by heart in 5 seconds max if you're a college student.

>>9105792
>2/36 = 1/18
>6/36 = 1/6
>Fraction Division, flip the bottom fraction then multiply.
>1/18 x 6/1
>6/18
>1/3

>>9105809
>>9105815
>>9105838

thanks guys

>>9105824

yeah i know, but as i said, i never paid attention during math in HS, so im trying to learn it as i go now.

>>9105792
>I never did well in HS math
>that was 5 years ago anyway

sure anon

>>9105857
Download Math Workout for your smartphone, it will help you do calculations faster. Practice frequently.

>>9102815
congrats, anon, you're illiterate!

>>9105678
stay poor and mad

>>9105895
I think it's due to physical intuitions. You simply need to use them to get better at math.

>>9105737
intuitions.com/physics/

>>9105737
I think the best way to learn is just to write up horrible puke inducing posts using physics here. Just make sure to keep the math at a very basic level and steal your stuff as the need inevitably arises.

>>9098951
I was wondering about physics textbooks. What are some good ones to get me started?
They should preferably have no math in them. If they do, then it should be primarily simple calculation and stuff which immediately follows from the definitions.

>>9106292
Physics is truly what this thread should be discussing. I'm thinking we should even go as far as to ban math.

>>9106400
I agree. We should ban that garbage from this thread.
Let's keep it clean :D

>>>/his/3245634

I can't prove the following. Please help

Let [math]G[/math] be a group, [math]n[/math] a positive integer, and let [math]H \subseteq G[/math] be the subgroup generated by all elements of order [math]n[/math] in [math]G[/math]. Prove [math]H[/math] is normal.

>>9106669
Go to worksafe request motherfucker.

>>9106669
literally trivial, what did you even try?

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>>9098951

With this, you are ready for University.

>>9106715
I have no idea, give me a hint. The only thing that I realize that such subgroup is isomorphic to free product of cyclic groups of order n. As this subgroup consists of all products of form [math]h = h_1h_2...h_n[/math] I have no idea why [math]ghg^{-1} = h' \in H[/math]

>>9106723
>The only thing that I realize that such subgroup is isomorphic to free product of cyclic groups of order n.
irrelevant

> I have no idea why ghg−1=h′∈H
the equality is trivial to prove, just ask yourself what you need to show for it to be true

>>9106723
Hint: what is the order of [math]ghg^{-1}[/math]?

>>9106723
following what >>9106737 said should get you the answer. A normal subgroup H is one which is invariant under conjugation by any element in G, i.e. if it is conjugated by any element in G, then the resulting element will be still be in H

>>9106737
Thanks, I remembered that [math]|ghg^{-1}|=|h|[/math]. But as some elements of [math]H[/math] may have an infinite order I can't make any conclusion

Why is the first method of finding the slant asymptote wrong here?

[math]\frac{x^2+x+1}{x+1}[/math]
[math]=\frac{x+1+\frac{1}{x}}[/math]
[math] ={1+\frac{1}{x}}[/math]
[math]=x+1[/math] as x -> infinity

[math]\frac{x^2+x+1}{x+1}[/math]
[math]=x+\frac{1}{x+1}[/math]
[math]=x[/math] as x -> infinity

>>9106751
>some elements of H may have an infinite order
How. The. Fuck.

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>>9106723
hint: [math] ghg^{-1} = \prod{gh_ig^{-1}} [/math]
You should be able to solve this

>>9106771
Whoops, first bit should be

[math]\frac{x^2+x+1}{x+1}[/math]
[math]=\frac{x+1+\frac{1}{x}}{1+\frac{1}{x}}[/math]
[math]=frac\{1+\frac{1}{x}}[/math]
[math]=x+1[/math] as x -> infinity

>>9106775
That's it, thanks.

>>9106771
[math] \displaystyle \frac{x}{1+\frac{1}{x}} = x - 1 + o\left( \frac{1}{x^2}\right) [/math] for large x, so the -1 cancels 1 from the other term.

>>9106772
Am I wrong? If [math]|g'| = x, |g''| = y[/math] it if possible [math]|gh|
= \infty[/math] or [math]|gh| = \text{your favourite number}[/math]

>>9101522
only if x*(x^2) = (x^2)*x is x^3 well-defined.
etc.

>>9101680
What do you mean by "exist"?

Doing measure theory for the first time and I can't get a grip on it, help please.

First I had to prove that a finite measure on a sigma ring is limited. That wasn't a problem

For the second part I have to prove that this measure can be extended to the sigma-algebra that is generated by the sigma-ring.
My first idea was to define the measure of the universal set and then go from there, but I can't even get that far.

For the first part I also proved that there is only a countable number of disjoint sets such that the measure of them is greater than 0.
I thought of defining the value of the universal set as the the sum of the measures of these sets. But the union of those sets is already in the sigma-ring, so I can't really do anything with them.

Any suggestions?

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http://aimath.org/textbooks/approved-textbooks/
Which of these would you recommend?
I've highlighted those I'd heard of before finding
this list.

>>9106876
Depends on what you want to learn, there's also a list of open books here
https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html
https://www.ams.org/open-math-notes
Or ya could always go to libgen

>>9106814
>Am I wrong?
Obviously.

>>9106995
[math]PSL(2, \mathbb{Z})[/math] is generated by two elements of order 2 and 3 and this group has elements of infinite order(for example product of generators)

Why snek lemma is such a meme

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I don't know how to read or even where to learn what the
( n )
( k )
thing is.

>>9107163
https://en.wikipedia.org/wiki/Combination
reads "n choose k"

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>>9106814
>"[math]|gh| = \infty[/math]"

Anyone can help me to find a paper with a proof that

[math]p_y(\boldsymbol{y})=p_x(\boldsymbol{x})|J|_{x→y} [/math]

where [math]J_{x→y}[/math] is the Jacobian matrix of x with respect to y?

>>9107163
It can be read as nCk
It can be interpretted as the probability of taking any given combination of size k from a population of size n.

>>9107517
what the fuck does this mean ?

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>>9098951
how do I find the antiderivate to sin(x)/x

>>9107559
[math]\int_0^x x^{-1}\sin x\;\mathrm{d}x=\operatorname{Si} x[/math]

>>9107550
I found what I needed.
https://en.m.wikipedia.org/wiki/Integration_by_substitution#Substitution_for_multiple_variables

>>9107559
First prove that it has no antiderivative in terms of elementary functions. Then get the Taylor series of the function and integrate term by term.

>>9107570
Nah, there is actually no proof. Can someone help?

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>>9107563
∫x0x−1sinxdx = Si x = 6

>>9107644
Nice пик

>>9107559
Start by taking your own subhuman frogposting life.

>>9101700
They can be built from set theory axioms, all from the empty set, which exists due to some axiom too.

Prove your dick exists.

>set theory axioms
I assume you mean ZF.
It's garbage. Probably inconsistent too.

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I don't really get the squeeze theorem, and I'm pretty sure I just showed it to be wrong.

What am I doing wrong?

>>9107982
from about halfway between your vertical line with x on it and the vertical line with a on it you dont have g(x) <= f(x)

>>9104622
It's like learning to juggle. You're just honing a technique most people don't bother with.

>>9107988
Oh, you're right.
I didn't understand the theorem properly.

I get it now.

>>9106751
lmao fucking what are you smoking no one in H has infinite order
reread the question faggo

>>9099470
you mean Catalan numbers
>t. combinatorialist

>>9108011

I haven't followed the thread of what was being discussed by a simple display of humility like this is always a welcome sight on 4chan.

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stuck here, how do i solve this/

>>9107517
It's Theorem 10.9 in Rudin's Principles of mathematical analysis. (if I understand what you're asking correctly).I'd say it's surprisingly tricky compared to the intuitive idea behind the formula

>>9107517
>>9108419
For the intuition, see https://math.stackexchange.com/a/464972

>>9108417
x^3 (x+5)^6 is a product. What is the rule for logs and products?

>>9108417
log(x*y) = log(x) + log(y)
log(x^a) = a*log(x)
why don't you read the fucking book you have, everything follows from those two if you remember y^(-1) = 1/y

>>9108424
Is it safe to download maths books in the uk?

>>9108443
idk, but probably. A proof can probably be found in other analysis books if you have one. If you have access to a (university) library, they'll probably have Rudin as well.

>>9108424
>For the intuition
The physical intuition?

>>9101522
>homomorphism
(ab)^n = a^n b^n holds iff the group is abelian.

>>9103259
Taking the nth root gives
[eqn]\left | x + y \right | \leq \sqrt[n]{n+1} \max(\left | x \right |, \left | y \right | )[/eqn]
for all n, which implies
[eqn]\left | x + y \right | \leq \inf_n \sqrt[n]{n+1} \max(\left | x \right |, \left | y \right | ) = \max(\left | x \right |, \left | y \right | ) \lim_{n \rightarrow \infty} \sqrt[n]{n+1} = \max(\left | x \right |, \left | y \right | )[/eqn]
as the sequence [math](\sqrt[n]{n+1})_n[/math] is decreasing and converges to its infimum of 1.

>>9105809
>>9105815
>>9105838
>flipping the bottom fraction
just cancel out the 36s retards, they're exactly the same

>>9107643
http://www.math.uiuc.edu/~r-ash/Stat/StatLec1-5.pdf

>>9108606
Intuition is that it works with sums over small segments => probably works with integration.

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>>9108693
Thanks, didn't think of doing something like that

>>9101339
>Axiom : All assumptions made in this proof are axioms.
Checkmate.

Brainlet trying to solve a physics problem here. Looking at a solution they have (v-w)^-2 dv/dt and simplify that to -(v-w)^-1 d/dt. What is this called, how does it work etc?

>>9109135
Just use your physical intuitions.

>>9108820
Obviously a black "person" wouldn't think of doing something like that.

>>9109171
I don't have any. That's why I'm trying to learn.

>>9109175
Black? wut

>>9109177
Cool. I love physics too. I hate math though lol

>>9109126
Right and wrong. Those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.

>>9109232
Elegant proofs don't exi-

>>9109231
What? You're an idiot. There's no lack of rigor in those proofs, making assumptions and being clear about them is what all of mathematics is predicated on. This is different from someone carelessly saying things and inadvertently assuming stupid things, and not being precise about what they do.
And who cares if mathematicians dislike physicists' lack of rigor? I'm sure the professional chef dislikes your mother's home cooking but your mother shouldn't be professing to be as good at cooking as him (or anything, really).

>>9109483
>What? You're an idiot. There's no lack of rigor in those proofs, making assumptions and being clear about them is what all of mathematics is predicated on. This is different from someone carelessly saying things and inadvertently assuming stupid things, and not being precise about what they do.
>And who cares if mathematicians dislike physicists' lack of rigor? I'm sure the professional chef dislikes your mother's home cooking but your mother shouldn't be professing to be as good at cooking as him (or anything, really).
It's copypasta you replied to

>>9109486
>It's copypasta you replied to
It's copypasta you replied to

>>9109491
From where?

>>9109498
Like there is a height threshold to determine who can post on /fit/, there is an intelligence threshold on /sci/. You don't meet it.
Please leave.

>>9105809
2.36÷6.36 is closer to .371 than to 1/3

>>9109507
Did you misread my post/mean to quote someone else? Your post doesn't seem to answer my question

>>9109532
it's not answering your question, but it's telling you that your asking of that question means you're missing something in the conversation

>>9109968
Please don't reply to my posts if you're not answering my question

>>9109498
Look it up in the warosu archive.

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>>9108697
We were explaining this shit to an idiot. Obviously I would have canceled them out normally, fuckwit.

What are good books for self studying vector calculus? I'm starting second year physics undergrad in a few months.

Trying to write proof for assignment
ran out of all english and greek alphabets because I'm shit
what do I use next? Hebrew alphabets?

>>9110364
frogpics

How do I into category theory?
What's a good textbook?

>>9110364
Use a different font. For example mathcal.

>>9110476
>mathcal
It's a hand-written assignment

>>9110480
Gross.
How long is this handwritten assignement if you've used that many letters?

>>9110486
I've already written 4 pages

>>9110364
Try using some physical alphabets.

>>9109483
Assuming anything without proof can only be used to prove that it is wrong.

>>9110476
>How do I into category theory?
I would say physical intuitions are a good place to start from. Category theory is a branch of physics anyway, just like everything else in math lol

>>9110390
This! We use frogpics all the time in physics hehe

>>9110325
You don't need textbooks. Just learn by doing experiments (simple ones, nothing too advanced) and advancing your physical intuition. That's all you need really.

>>9102098
Subset axiom or >>>/gtfo/

>>9110529
>4 page handwritten proof
Why don't you just index your letters?

There is no physics or a dumb question general, so i ask this here:

Why is distance per time expressed as distance/time in math.
I know this sounds extremely silly, but i guess its more a problem with fully understanding what a fraction or division means.

Generally i have problems with fully grasping why quantities are related a certain way in a physical formula.
So why is "per" translated to a fraction?
Or why is a slope x/y?

>>9110627
*y/x sorry

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What am I in for?

>>9110644
> What am I in for?
analysis and set theory

>>9110644
Set theories are known to be garbage.

What's with all of this physics talk in these threads?

>>9110873
We just like to discuss our physical intuitions.

>>9110543
What do you mean by experiments? Vector calc was my bane during the E&M course last semester, and I just want to be prepared ahead of time for second year.
I just want a book that explains the theory well and has good excercises to practice.

>>9110908
>What do you mean by experiments?
Fuck that math shit. Just perform some experiments to learn vector calculus. You don't really need math to understand it.
You should be spending your time mastering your physical intuitions, not doing math.

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>>9110926
>mfw fell to bait

Mathlet here. Recently I have been studying different video series about financial time series data analysis. I don't know very much about statistics but I'm interested in learning more about what they are doing. I'm not sure what it's called but basically what they are doing is using excel to calculate standard deviations and intervals to draw histograms and find out what is normal and what is abnormal and how economic data like GDP and employment relates to S&P500. So where can I learn more about this?

>>9110644
Throw it into the trash and buy Elon Lages' book on Analysis, if you can't read in portuguese then too bad you'll have to make due with that Landau trash.

>>9111266
What for? I guarantee you, you won't make any $$$ on it.

>>9111266

> it's another idiot who likes to foam at the mouth thinking about numbers with dollar signs attached and thinks he belongs on this board

Why is math so beautiful anons?

>>9111372
It isn't. Physical intuitions are what is truly beautiful.

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Brainlet here. I was asked to derive the quadratic formula. The fuck does that even mean?

>>9111482
Take ax^2+bx+c=0 and rearrange until it is the quadratic formula. p easy shit senpai

>>9111482
ax^2+bx+c=0

solve for x

>>9111482
You won't be able to do this >>9111488 >>9111490 unless I tell you to complete the square, if you're new to maths.

>>9109976
>>9110364
German Fraktur

>>9111490
>>9111488
Not him, but how do you find the roots of an equation by factoring without guesswork? I'd assume that would be impractical if I have a high order equation. I need to understand this for unit root tests

>>9111570
>how do you find the roots of an equation by factoring without guesswork?
Try using your physical intuition.

>>9111651
let me know how that works for you for the biquadratic and quintic equations

>>9106876
literally not a single book on that list that i would recommend for those subjects
what the fuck kind of fraud institute is that?

>>9112474
>implying you've read any of those books

>>9112476
>implying i need to read garbage to recognize it
hello, new

If I have some solutions [math]a_k, b_k[/math] for the equations:
[math]\sum_{k\in K} \cos(\alpha a_k)=\sum_{k\in K} \sin(\alpha b_k)[/math]
[math]\sum_{k\in K} \sin(\alpha a_k)=\sum_{k\in K} \cos(\alpha b_k)[/math],
where [math]K=[1,2n], \alpha = \frac{\pi}{2m+1}, n,m\in \mathbb{N}[/math].

Does it follow that each individual sum is 0?

>>9112486
Forgot to mention, [math]a_k, b_k[/math] are integers too.

>>9112476
>Analysis with no mention of Rudin
>Differential Equations with no mention of Arnold
>Logic with no mention of Mendelson
>Set Theory without Jech or Kunen
yeah nah it's fucking trash

>>9112490
>implying any of those books are open source
Do you even know how to read?

>>9112484
>judging a book by the cover
hello, new

>>9112490
>Rudin
>good

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Can anyone explain this to me ?

>>9112917
which part?

>>9112917
are you french ? I'm too lazy to translate this

>>9112921
Preferably, the entire proof.

>>9112924
Yup.

>>9098951
Is physical intuition just some kind of cohomology theory?

So my math book is trying to prove that [math]arctan(x)d/dx=1/(1+x^2)[/math] .
It does this by stating the following:

[math]arctan(x)=y<=>tan(y)=x[/math]

[math]arctan(x)d/dx=dy/dx=1/dx/dy=1/tan(y)d/dy=1/(1+tan^2(y))=1/(1+x2)[/math]
I don't understand the second last part, shouldn't it be [math]1/tan(y)d/dy=1/1/(1+cos2(y))=cos2(y)[/math] ?

>>9112984
Fuck, I'm to tired to manage these fucking [math] tags... Hopefully someone will be able to decipher what I'm trying to say.

>>9098951
life is just one big combinatorial problem

>>9109232
How is that proof?

>>9112917
its a basic statement about the properties that primes have.

for theorem 4.

if we take our Z to be 2, and exp it by some prime p, say for instance 5. we get 2^5. which is equal to 32. now 32 we count mod 5.

(12345,12345,12345,12345,12345,12345,12)

our 32nd count lands on a 2. giving us a^p = a mod p.

do this with any combination of a on Z and p on primes and you will get the same thing.

essentially, all we are saying is that primes are an invariant.

Is it a really bad sign for the math community that it's been 5 years since Mochizuki's alleged abc proof was released and it still hasn't been verified or debunked by anyone? abc is a huge result and it's as if no one actually cares about a possible proof

>>9112498
>open source
you don't know what open source means
seems like it's you that doesn't know how to read

>>9113446
>you don't know what open source means
>seems like it's you that doesn't know how to read

http://aimath.org/textbooks/evaluation-criteria/
what part of "To gain our seal of approval an open source mathematics textbook..." goes over your head brainlet?

>>9112498
>preferring books that abide by some dumbass """evaluation criteria""" instead of selecting the best and/or standard/definitive texts for each subject area
spoken like a true bureaucrat

>>9113448
hmm i guess the part where they never define what Open Source means in this context and that, without an explicit definition for what they mean by it here, "Open Source" is a meaningless term in this context
faggo

>>9113450
What other "dumbass evaluation criteria" are you not allowed to use to make lists? Can I not make a list of analysis books specifically for undergrads either?

>>9113453
If only you knew how to read.

"A book is open source if the source file(s) are freely available for others to download and use."

Does that still go over your head, brainlet?

>>9113465
woah except for the fact that every book i listed is "freely available for others to download and use"
that notion is not precise, nor legal, and has nothing to do with the way the term "open source" is used legitimately in other contexts
borrow a few IQ points from your neighbor before continuing to reply to my posts

>>9101517
They already have that, look up "nonlocal equations"

>>9113469
>woah except for the fact that every book i listed is "freely available for others to download and use"
Please link the source file for even just one (1) of the books you listed.

I'll wait, brainlet.

>>9113463
I'm not saying you're not allowed to do whatever you want, I'm saying that almost every single definitive or highly-regarded text for the fields they've listed is omitted from their list, despite the fact that many of these books are either cheap or free (eg. Arnold's Diff Eq)

Regardless, it's also stupid pedagogically in my opinion to recommend books to students based on some stupid notion like open sourcedness instead of quality and relevance

>>9113476
>I'm saying that almost every single definitive or highly-regarded text for the fields they've listed is omitted from their list, despite the fact that many of these books are either cheap or free (eg. Arnold's Diff Eq)
Because they're not open source... why is this confusing?

If I make a list of undergraduate analysis books it would be equally inane to complain that highly-regarded graduate texts are absent from the list

>>9113472
nah, you can just google "[book title] pdf"
i'm not doing your laundry for you, faggo

>>9113480
So not a single one of the books you listed are open source, glad we agree.

Please learn what 'source file' is before posting again, brainlet.

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>>9113479
According to their asinine definition, yes, they are open source.
And your second claim is completely unrelated, since you're now suggesting recommending books for a subject that don't really fall under that subject heading.

>>9113482
Looks like you didn't read their definition of open source. Glad you don't know how to read.

>>9113482
point to me where on the doll they defined "open source"
oh, they didn't? nor did they define "source file"?
glad we agree, brainlet

>>9113486
>Looks like you didn't read their definition of open source. Glad you don't know how to read.
see: >>9113465
>"A book is open source if the source file(s) are freely available for others to download and use."
Still waiting for a link to the source file for any of the books listed above.

>>9113490
>point to me where on the doll they defined "open source"
see:
http://aimath.org/textbooks/guide-for-authors/
Please learn to read before posting again, brainlet.

>>9113491
Listen, if you want to be intentionally obtuse that's none of my concern, but don't you dare ever reply to any of my posts again.

>>9113486
>According to their asinine definition, yes, they are open source.
Where's the source file for Arnold's book?

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Anyone have some good hints/tips for this problem?

>>9113496
>Listen, if you want to be intentionally obtuse that's none of my concern, but don't you dare ever reply to any of my posts again.
What's obtuse? The list is for open source books, you listed closed source books (feel free to prove otherwise by linking to a single source file).

>>9113497
since you haven't defined "source file," the source file is right here embedded in this 4chan post

>>9113500
I thought I told you to never reply to my posts. I won't say it again.

>>9113501
How do I compile Arnold's textbook from your 4chan post?

>>9113503
>I thought I told you to never reply to my posts. I won't say it again.
Where's the source file?

Aren't your books open source?

>>9113505
it should be obvious once you define "source file"

>>9113509
>it should be obvious once you define "source file"
See: https://en.wikipedia.org/wiki/Source_code

>>9113509
>it should be obvious once you define "source file"
http://lmgtfy.com/?q=define+%22source+file%22

>>9113511
>>9113512
woah sasuga, anon! two completely irrelevant definitions that don't pertain to the subject at hand!

>>9098951
A pretty shit thread you've got going here.

>>9113515
Which part of the definition confuses you?

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>>9113516
>expecting anything out of math threads on fucking 4chan

>>9113517
the part where AIM defines what they mean by source file
just go ahead and give me a screenshot of where they explicitly define this term

>>9113516
>>9113521
It's a good thread when you contribute to it.

Can you build a function that behaves like this:

Can someone give me a function f(x) that behaves like this?

f(1) = 1
f(2) = 2
f(3) = 3
f(4) = 1
f(5) = 2
f(6) = 3
f(7) = 1

and so on?

>>9113521
Did you reply to the correct post?

>>9113524
It's the standard definition that everyone uses.

Do you want a definition of 'textbook' and 'math' too, brainlet?

>>9113525
>Can you build a function that behaves like this:
Yes. It's trivial and not worth discussing.

>>9113529
glad you've conceded the argument
you may now return the borrowed IQ points to your neighbor

>>9113537
You not knowing what 'source file' means just means you wouldn't know open source from closed source anyway.

This is exactly why you think Rudin and Arnold are open source when they're not (feel free to prove otherwise by linking to a single source file).

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>>9113525
uhh, you just defined the function right there?
you should rephrase your question, because otherwise there really is nothing to discuss in your "contribution"

>>9113525
>Can you build a function that behaves like this:
Not until you specify its domain and codomain

>>9113539
>uhh, you just defined the function right there?
I realize that it might be difficult to understand for a CS-tard, but "=" means something different in Mathematics.

>>9113546
do you have brain damage?

>>9113548
Nope, not that I know of. What made you think so?

>>9113538
>feel free to prove otherwise
You didn't prove the negation of his statement, feel free to prove it before posting.

>>9113553
>You didn't prove the negation of his statement, feel free to prove it before posting.
Wrong.

Burden of proof is on him/her since he/she posted them as being books that should be on the open source list.

>>9113557
>Burden of proof
No such thing exists in mathematics.
Feel free to fuck off to >>>/lit/ or even >>>/r/eddit since you seem to like their spacing style so much.
>him/her
>>>/r/eddit/

>>9113557
>burden of proof
lmao thanks for confirming you've never actually done mathematics in your life

>>9113559
>No such thing exists in mathematics.
Who was talking about mathematics?

>>9113560
>lmao thanks for confirming you've never actually done mathematics in your life
See above.

>>9113563
>not understanding the relationship between logical propositions and mathematics
christ i'm losing iq points just reading your posts

>>9113563
>Who was talking about mathematics?
This is a mathematics thread. That is why I told you to fuck off to >>>/lit/
You can discuss your petty word games and "burdens of proof" there. This is exclusively a Mathematics thread and non-math garbage will not be tolerated here.

>>9113567
What's the mathematics behind the source file you continue to fail to produce? All you have to do to prove your claim that the books are open source (reminder: the burden of proof is on you since you made the claim) is to produce a single source file (as per the definition of open source).

>>9113568
>This is a mathematics thread.
Yes.

That's why we're discussing math textbooks.

Still have an issue?

>>9113571
>That's why we're discussing math textbooks.
Math textbooks aren't mathematics. Feel free to discuss them on >>>/lit/ (a place which is actually meant for discussing books).

>>9113571
>still hasn't defined source file
rofl

>>9113571
>math
>"burden of proof"
>>>/lit/
We demand rigor here.

>>9113572
>Math textbooks aren't mathematics. Feel free to discuss them on >>>/lit/ (a place which is actually meant for discussing books).

Your concerns aren't mathematics, feel free to discuss them on >>>/qa/ (a place which is actually meant for discussing concerns)

>>9113576
>>still hasn't defined source file
see above: >>9113512

>>9113581
>see above: >>9113512
see above: >>9113515

>>9113577
Yes, rigor is required to prove that a textbook is in fact open source.

Feel free to link to one of the source files for any of the textbooks you listed above.

>>9113539
Obviously, the function extends infinitely in the naturals. Listing the function that way isn't rigorous (and doesn't count as a closed form), as you very well know.

>>9113584

What part of the definition still confuses you?

I can help you through this one step at a time if such thoughts are too difficult for you, brainlet.

>>9113587
Yes but it's so fucking trivial to define I'd rather berate the poster than spoonfeed him

If you're the poster then here's a hint: think in mod 3

>>9113589
>posting the same replies to the same arguments
are you a faulty AI?

>>9113530
Pretty please?

>>9113542
This is not the time for pedantry. f: X → Y. And if you can't see the pattern, I doubt you'd be able to answer my question anyway.

>>9113597
Wouldn't faulty AI post different replies to the same arguments.

Also what you are posting is hardly an "argument" by any definition of the word.

You not understanding a definition is not an "argument".

Neither is your failure to produce a source file.

>>9113598
Who are X and Y?
The fact that you think anyone would have trouble answering your question, along with that statement, show me how misguided you are.

If you really want someone to take the time out of their day to respond to something they already told you is fucking trivial you should at least be polite about it, faggot.

>>9113608

>If you really want someone to take the time out of their day to respond to something they already told you is fucking trivial you should at least be polite about it, faggot.

Why the homophobia?

>>9113600
nah, a properly functioning AI learns, unlike you

File: 20841139_1392179827564042_2874412870342691408_n.jpg (59KB, 960x768px) Image search: [Google]

59KB, 960x768px

>>9113612

>>9113613
Why would an AI do anything other than link a definition when someone is confused by a word?

>>9113608
>Who
Ok, now I'm confused. All I'm asking for is a function that fits these criteria:

f(1) = 1
f(2) = 2
f(3) = 3
f(4) = 1
f(5) = 2
f(6) = 3
f(7) = 1

Surely you see the pattern that describes f(x).

Can you please help me *define* f(x) ?

>>9113612
>reddit spacing
>homophobia
>>>/r/eddit/

>>9113592
I considered mod 3, but mod 3 has a 0 every three elements. I essentially want f(x) = x mod 3, but where multiples of 3 are 3 and not 0. I can't just add 1 because that ruins the rest of the numbers.

What am I missing?

>>9113621
What is the domain and codomain of said "f"?

>>9113623

Where is the source file?

>>9113621
So we'll assume [math]f: \mathbb{N} \to \mathbb{N}[/math] then and that [math]f(0) = 0[/math].
What do you notice about your function?
The first thing you should see is that every multiple of 3 gets mapped to a multiple of 3. Likewise, every multiple of 3 minus 1 is mapped ot a multiple of 3 minus 1, and every multiple of 3 minus 2 is mapped to a multiple of 3 minus 2.

>>9113626
okay so you're on the right track. I suggest you rethink whether or not you can simply add 1.