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>There are no numbers less than zero
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You are currently reading a thread in /sci/ - Science & Math

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>There are no numbers less than zero
>There are four operations: add, subtract, multiply, divide
>You can't divide all numbers evenly
>Negative numbers don't have square roots
>Parallel lines never cross

>Atoms are the fundamental building blocks of matter
>Protons, electrons and neutrons are the fundamental building blocks of matter
>Electrons orbit the nucleus
>Hunds Rule
>Find molecular shapes with VSEPRT
>Noble gasses can't form compounds

At what level do my math and science teachers stop lying to me?
>>
>>7763783
never
>>
When you stop going to class fucktard.
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>>7763783
If you view every rule that actually has an exception or weird edge case, or holds only under common conditions or assumptions, as a "lie", then never.
>>
It would be nice if teachers pointed out that the things they are teaching about are actually more complicated, but it doesn't help the student understand the simple explanations, and that insistence on correctness can mean a lot of extra syllables in awkward places.
>>
Parallel lines never cross
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>>7763813
He's talking about some weird 'projection plane' bullshit that states that if you extend the lines to infinity, they will eventually touch.
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>>7763783
When you're teaching a kid what sound the letter "g" makes, you probably don't want to immediately bring up words like gnome and through. It's unnecessary confusion at that point. Just like a lot of your examples would be.
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>>7763817
No, he's talking about non euclidean geometry.
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>>7763899
Same thing retard. Projective geometry is one type of noneuclidean geometry.
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>>7763934
My bad.
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Can someone explain the "division and subtraction do not actually exist, you're really just adding a negative and multiplying be a fraction" thing? I know they effectively give the same result, but why that theory behind it? What is logically wrong about subtracting and dividing?
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>Parallel lines never cross
But they don't
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>>7763946
How is high school geometry working out for you, pleb?
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>>7763948
But in euclidean space they never do
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>>7763949
That is what OP meant. There are non-euclidean geometries that students are never taught anything about. They teach you properties of the euclidean plane like if they were set in stone and the one and only truth of the universe when in fact, nowadays we might as well call euclidean space the trivial space.
>>
When you understand that maths is not about "true" or "false" statements, you will understand that no math teacher ever "lied" to you, they just taught you différent parts of maths.
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>>7763943
We try to DEFINE things as simple as possible, so you don't need to remember much of these often quite arbitrary definitions. E.g. we define a group as a set with a SINGLE operation or a field needs two operations that satisfy certain axioms i.e. commutativity/distributivity. If we also introduce minus and divide by we also need to state these axioms for the new operations, which would make the list of things we need for a formal definition quite long.

Ofc you could do it, but it is not needed, so we keep it simple.
>>
>>7763949
Not everything is a euclidean space.

>>7763943
Subtraction and division are not operations which need to be defined separately from addition and multiplication. When defining a thing you say here is the operator (+) and here is what it does (a + b = b + a, a + 0 = a, a + -a = 0, etc). You can see the definition of subtration is already there in the definition of addition, and like wise division is alrrady a part of multiplication (a * 1 = a, a * 1/a = 1)

You may argue that multiplication is not an operation which needs to be defined, however it does not have to follow the same rules as addition. Matrix and vector multiplication for example do not follow the same rules as addition. Same thing with function multiplication (you could define f() * g() to be f(g()) + g(f()) but we don't, just for example, and therefore multiplication is a necessary definition.
>>
Never, because there is no objective truth to anything, only theories. Most professors have learned theories from books that were written years ago, which are now outdated. There is no "god given theory which answers everything" (yet?).
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>>7763966
So could I make a "math" where I define subtraction, and just say addition is a special case of subtraction?
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>>7763970
>2016
>still people who have never read the Bible
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>>7763972
No, you can define an operation called - on the set of real numbers which acts like subtraction, and has the same properties as addition, and it would make no difference except you would need extra -1 multipliers everywhere.

And then you would find, in the set of operations on R, there exists +, which has all thoae properties and doesn't require -1s everywhere, and you would use that instead.
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>>7763972
Interesting. I struggled through some college math like many people and will admit I never understood the concept of imaginary numbers at the time, I was just like, what a concept, I don't even want to try, sounds ridiculous.

>>7763977
Made it into Gensis and was like, meh, talking snakes, 1000 year old men - there are people who take this shit literally. I grasp the allegorical nature of it but read the Hobbit instead I think as a kid, as I grew up I found the Greek philosophy that predated it far superior. In fact it's spooky what happened to humanity, the grip of the dark ages culminating in Black Death - wew lad!
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>>7763972
Yeah, you kind of can. It would be really dumb because it is so fucking counterintuitive, but you certainly can. The funny part is though, that once you have defined subtraction you can simply define additio" exactly the way we currently define subtraction just by switching the words subtraction and addition.
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>>7763790
fucking gold
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>>7763999
Addition would be cases of subtraction that are commutative.
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>>7763997
>imaginary numbers
It's like this. You know how lines can be perpendicular? The imaginary numbers are a number line going through 0 which is orthogonal (for the most part means perpendicular) to the Real Number line. Together they form the complex plane.
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>>7763972
These are the interesting kinds of questions that abstract algebra formalizes. It really is a very interesting subject and the basics aren't too tough if you want to learn some.
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>>7764008
>going through 0

But doesn't -i = 1? Wouldn't the line stop at 0?
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>>7763960
If they say it's impossible to subtract bigger number from the smaller one or that square roots of negative reals don't exist they pretty much do lie
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>>7764015
>But doesn't -i = 1?
No.

There are several ways of viewing complex numbers:
1.) We want all polynomials to have solutions, so we add in all solutions to polynomials to the real numbers. This is incredibly useful, and gets used a lot.

2.) Take a copy of the plane and define multiplication by rotation and you get the complex numbers.
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>>7763966
In high school it is though
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>>7764008
Well that is only half the point. If you want to define the imaginary numbers that way you have to say how two such numbers multiply, which is slightly twisted, therefore I prefer the i approach.
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>>7763783
Some of these lies are ok, like teaching kids that parallel lines don't cross. non-Euclidean space is an idea most people won't ever need and aren't equipped to deal with in high school anyway.

The average high school math class doesn't have the firepower to do much interesting with i so it's mostly a pointless formalism at that level.

Lies in science are worse because usually it's not that they're leaving out a weird, counterintuitive case, it's that they're teaching you flat-out wrong models.
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>>7764020
They don't teach you about cones and spheres in high school in US? Not shocking to be honest.
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>>7764029
Lies in Science are more necessary in High School because of the Math required to know the truth is well beyond the student.

I mean, the Bohr model, which wrong, is at least in the ball park, compared to the pudding model.

And it's not like Newtonian physics do not accurately describe most situations.

Relativity and quantum mechanics are in fact the edge cases of science, the very small, very fast, or very dense objects.
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>>7763970
>CANT NO NUFFIN
But seriously, if you begin with a set of axioms and use deductive reasoning to derive results from these axioms you are discovering truth.
In the natural sciences its obviously different. You use models supported by data to explain phenomena that occur in the universe. This is not always perfect and needs to be refined again and again.
In mathematics, if a valid proof is given, you have learned something fundamental about what you are studying.
>I took the b8
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>>7763977
I've actually read the bible cover to cover (took me fucking forever). Not very convincing I'm afraid :(
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>>7763838
gnome has a silent g? I always pronounced it as gunome
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>>7764060
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>>7763783
what's wrong with hund's rules?
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>>7763997
>Gensis
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>>7764079
There are a few funky transition metals that have lower energy states filling complete specific d-orbitals before putting an electron in another one.
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>>7764033
And they're objects in three dimensional euclidean space
>>
>>7764060
Haha. Thanks for the laugh.
>>
>>7764094
That's the Aufbau principle, it's for working out what electronic configuration an atom or ion will have. Hund's Rules are for a given electronic configuration, and they generally work very well.
>>
Are negative numbers a jewish conspiracy?
>>
>>7764215
They were invented specifically to track debt.

You decide.
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>>7763783

>Noble gasses can't form compounds

>Xenon Difluoride
>>
>It is not scientifically proven that God exists
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>>7764336
Did you read the rest of the post, you illiterate fuck?
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>>7763943
>44,8998886413^2
>Not knowing subtraction is just a + -b = a - b.
>Not knowing division is just a + 1/b = a / b.
>>
>>7763783
when you're out of highschool
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>>7763783
The more I see here the more I realize how lucky I was to get such great high school math teachers, really.
One of the things they covered was this, saying that they never wanted to use "always" or "never" when teaching us math because there was an exception almost every time, so we should just take it as it is and understand the usefulness of the math we know with the understanding that we could gain a deeper understanding of it later.

>>7763800
This is a really simple example, but teaching a kindergartner about negative numbers isn't going to be helpful. Kids that age don't have any need or reason to understand it, and it would not make nearly as much sense to one as it would to a 3rd grader. Teach him addition and subtraction however, and everything makes sense. Negative numbers are an abstraction of addition and subtraction essentially.

Now consider why we don't necessarily teach courses on topology to people studying engineering, even though all the math they ever do can be abstracted to just an application of topology. They have no reason or need for it and it doesn't apply to them, so they're better off working just within a system that makes sense to them instead of the more abstract mathematical reality.

All of mathematics is taught like this.

If you really want to get to the bottom of your question, OP, start by learning logic. Logic is logical and nobody can lie to you about that if you understand it. From there you can read about how mathematics is constructed from that so nothing you learn is without some logical basis and then nobody can lie to you about math again.
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>>7764420
Nope. Engineers and scientists in college eat up "lies" which make mathematics easier for them to understand all the time because having them take a bunch of topology classes to get the bigger picture behind the space that they work in is "too hard." Most of the concepts the analysis students take as intuitive are, although logical, dependent on much more abstract concepts which are simply not talked about.

This is analogous to OP's idea that his teachers are "lying to him" by glossing over things to make them simpler for him to understand.
College does to the same thing to literally everyone that doesn't study math because it makes more sense to teach that way.
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>>7763783
>be me
>8th grade
>ask too many questions about gravity
>teacher thinks we'll all overthink the next test and fail because of me
>tells class gravity is caused by Earth spinning
>admits it was a lie after the test

What the fuck, man
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>>7764060
I found the American.
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>>7763783
>>There are four operations: add, subtract, multiply, divide

In reality, there are jus 2 operations. That's what my professor told me atleast.The other 2 are varied forms of the former 2.

>It really makes more sense that way
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>>7765241
It's easier to add negative, because adding negatives is commutative.
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>Negative numbers don't have square roots

this is true though

the concept of numbers has always existed, even before man discovered them. the concept of an"imaginary number i" is just a man made term, like a God of the gaps argument

if i take a pizza, and give 100% of it to person A and "imaginary pizza 'j'" to person B, i could say that person B has been given j pizza, and just because i said j pizza exists but its imaginary, then its still true

same deal with "abiogenesis". just another word for "magic fairydust" or "something i can't explain so here's a science term to make you think i can explain it"
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>>7763783
>All the math stuff
Exactly what happens when you begin with a special case and then generalize to more interesting case.

>All the science stuff
That's because science is retarded, anon.
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>>7764060
It is, just like in gunu plus linux.
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>>7765244
Just have seen a proof and some example for that.
You could even change the negative number system with just positive numbers. For examples 0 (negative) & 1 (postive) as a substitute.
0~4 could be for example -4.
1~2 could be 2.

It's trivial and I tell you nothing new but it would have been really nice to see such examples in school just to get a better grisp for examples and applications. Like, how it would affect Turing Machines and such and how numbers can work and how they 'can' interact.
Just a better concept of numbers.
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>>7765241
I think he was talking about elementary school when the teacher would claim there are only 4 operations.
And at that point they also claim there are no numbers smaller than 0, therefore you can't derive subtraction from addition.
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>>7765245
But unlike your pizza example, there is stuff in physics that won't work without i. A square root of -1 must exist. You could say that our number system fails to intuitively represent math as those relationships objectively exists in the universe.
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>>7763997

The snake isn't actually a snake, look into the original language a bit more and you'll be surprised what you might find.
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>>7765261
It's a talking penis, which is slang for a black guy. Eve loved that BBC.
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>>7763783
>Parallel lines never cross
They do?
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>>7764033

Yes of course they do. Geometry was covered in the 10th grade for me. Basic stuff was teased as far back as 7th grade.
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>>7763948
>implying that all geometries are projective

How is community college working out for you?
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>>7764016
negtive numbers dont exist when you are working in non-negative reals/integers

sqrt negative numbers dont exist in the reals
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>>7765282
Imagine a sphere, a globe. Take any two lines perpendicular to the equator. Since they are perpendicular to the equator, they are parallel. Now extend them to the north and south pole. The lines meet. Same thing on a cone.

>>7765301
See above. Spheres and cones are non-euclidean spaces.
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>>7763783
Τeaching maths intuitively is the biggest mistake. Most people fail with maths just because they try to find a correlation to the every-day life. If you try to understand higher level maths by reasoning with the tangible world it all becomes a mess.
In my opinion, even elementary level maths should be teached axiom-style and not abacus or pie-related. Children mustn't let the real world interfere with mathematic logic.
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>>7765637
>non-euclidean spaces
Ιt's called euclid geometry because we only talk about planes. Therefore it isn't wrong that parallel lines never cross
>>
At the moment they repent trying to make you insecure and dumb.

>everything is taught in a way that it can be discarded
>it makes your life harder because at any moment, just like the Quran, a new statement will replace an old one
>even the basics are not taught well
>its harder for you to take anyone seriously at any level, because the next level might fuck your shit up. so you instinctively don't learn
>you have specialised teachers, yet you must learn all their knowledge. So technically you graduate better than all your teachers. And technically, because of their specialisation, the teachers could teach you the truth from the begining, instead of a simplified version of it.
>teachers are trained to waste as much of your time as possible
>teachers are bad at basic logic and are trained to oppress students
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>>7765652
Yeah, and it's called Geometry because we talk about Spaces, not limiting ourselves to planes and straight lines.
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>>7765664
w/e
Everything works this way in mathematics. I'm not trying to convince you here, what matters is the definitions. Parallel lines don't cross in standard logic. But you're right as well.
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>>7765655
*tips fedora*

The Qui'ran is the final revelation you fuckload faggot edgelord.
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>>7765668
The definition of two lines which are parallel is the following:

Take a single line. Allow two other lines to cross the first. The two lines are considered parallel if they cross the first line at the same angle.

The fact that they will never touch is only true in euclidean spaces, and requires a proof, it is not a part of the definition, and is simply not true in spaces with curvature.
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>>7764410
> a + 1/b = a / b.
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>>7765637
The very definition of parralel lines is that they never intersect. So already we have proven that parralel lines do not intersect ( any lines that intersect are not parralel) just because two lines are perpendicular to a sphere's equator does not mean they are parralel with eachother. You cannot apply the rules of a Euclidean space to a non Euclidean space.
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>>7765668
>parallel lines dont cross in standard logic

you don't know what parallel lines are, you have never studied geometry, do not talk about things you have not studied (specifically, don't ever say "standard logic" again)
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>this troll again
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>>7768030
The lines [math] \{(t, 0, 0) | t \in \mathbb{R} \} [/math] and [math] \{(0, t, 1) | t \in \mathbb{R} \} [/math] are not parallel and still don't intersect.
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>>7763783

Wittgenstein's ladder

You gotta throw away the ladder once you climb up
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>>7768030
Have you read the parallel postulate?
>If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

The definition of Parallel is the converse of this statement. Two lines whose interior Angles, when crossed with a third line, sum to 180 degrees.

That's it. Let me repeat Parallel Means:

Two lines, whose interior angles when crossed with a third line, Sum to 180 degrees.

This is true in every geometry, Euclidean, Hyperbolic, Elliptical, whatever space you can come up with. If you have two lines, and they are crossed by a third line, and the interior angles is equal to 180 degrees, they are parallel.

That the 5th Axiom does not hold on a Sphere is the difference between Euclidean Space and a curved space. It has nothing to do with whether the lines are parallel.
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>>7764077
What's the problem, in french it's pronounced that way. The retardation here is reacting like you to that mistake.
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>>7763813
2 parallel lines can be thought as 2 spheres with infinite radius
thus the sphere definition would provide they both meet @ infinity.
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>>7765260
Things work without i, but expressing them without it is just way more complicated.
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>>7763783
ok I need help explain these for me
>There are no numbers less than zero
>Electrons orbit the nucleus
>Hunds Rule
>Find molecular shapes with VSEPRT
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>>7763783
Never, because current human knowledge is just an approximation of what really goes on in the universe.

They'll just tell you enough so that you can get to the next level.
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>>7764420
>limits of sequences are unique
>The closure of a point is that point: [math] cl\{p\} = \{p\}[/math]
>You can't talk/reason about the collection of all sets/groups/rings
>Statements are either true or false
>Affine space over a finite field has finitely many points
>There are no infinitely large natural numbers

Just a few university lies. But as other people have pointed out, they're not so much wrong as specific to a certain situation, like how there are no numbers less than zero when working in the monoid/rig of natural numbers.
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>>7768039
Is it possible to have perpendicular lines that don't intersect?
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>>7768519
Not in plane or spherical geometry. Probably not ever, but I'm not sure.

It of course depends on the definition, but a lot of the time the definition of "perpendicular" is tied in with the definition of intersection.
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>>7768150
>Statements are either true or false
This isn't true? How is this not true?
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>>7768527
It's neither true nor false.
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>>7768530
How can something be neither true nor false? Isn't that one of the fundamental building blocks of logic?
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>>7768524
So a line on the x axis and a line raised up one unit and rotated 90 degrees would not be perpendicular?
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>>7768531
https://en.wikipedia.org/wiki/Many-valued_logic
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>>7768535
Didn't think about that one. Pretty sure it would be, I was thinking of plane geometry and sphere geometry, as I said. Operating in 2d space.

In 3d space for example it is impossible for a PLANE to be perpendicular to another PLANE without intersection, and so on for objects on n-1 dimensions in n-dimension spaces.
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>>7768531
If you're a computer, yes. But there are shades of grey. Computer Architecture can not interpret a three position switch, so it needs to be broken down into up (on/off), middle (on/off), down (on/off). But the human mind can just see and interpret up, middle, or down.
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>>7763954
Can confirm.
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>half of /sci/ posters apparently don't know what parallel means
>outsiders actually think this board is about science and math
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>>7768541
>>
>parallel lines cross in muh special plane
>sum of all positive integers is -1/12

Remind me why we fund math again?
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>>7768808
Because math is why we have useful technology. Or actually inb4 pure mathfags attack me, applied math is why we have useful technology. And if stupid psuedoscience shit like psychology gets funded, why not mathematics?
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>>7768092

literally this

why is everyone so hung up about complex numbers like theres some great mathematical philosophical memery going on in nature

it's literally a notational (and thus computational/analytical) efficiency

it's a fucking great and useful efficiency

but it's just that
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After 13 years in Chemistry academia:

Chemistry is the science of progressive lying.

That's all there is to it.
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>>7769189
>it's literally a notational (and thus computational/analytical) efficiency
You've never studied anything remotely interesting if you think this is true.
Even taking babys first QM course it's pretty easy to see that there is some memery going on.
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>>7769189
>I've never heard of quaternions
>I've never done EE
>I've never done QM

Please, keep spouting your ignorance. I'm having a good laugh.
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>>7769189
Tfw I only work in the octonians :(
>>
>There are no numbers less than zero
>There are four operations: add, subtract, multiply, divide
>You can't divide all numbers evenly
>Negative numbers don't have square roots
>Parallel lines never cross

What you're taught in school is a particular case of a particular case [...] of a particular case. Nowhere in the study of mathematics will you be able to study what things really "are". You may think "well, abstract algebra is the foundation of modern mathematics", and that could be said about topology as well, but then you realize that they also are a particular case of some higher structures in category theory. Even then, you realize that piling abstractions over abstractions could possibly never reach an end. Set theory, for instance, is a very good tool but it's limited. Algebraic topology is brilliant too, but it's limited.
You must change your point of view! The duality in mathematical structures is what will make us make true discoveries in the future, and possibly will make us have better insights about mathematics. Duality is not necessarily symmetry. Symmetry is a particular case of duality. The mathematic of the last century is (soon?) to be erased by someone who will finally understand how structures are related. And moreover, why are there structures? Why do morphisms work so well in some cases and so bad in some others? There are so many questions to be answered. Questions which are asked in the wrong way, of course.

tl;dr bitch all you want about how maths are taught and wank over your pointless undergraduate definitions, you will never ever EVER understand mathematics. Fuck you.
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>>7769189
[math]\mathbb{C}[/math] is the algebraic closure of [math]\mathbb{R}[/math], which is the completion of [math]\mathbb{Q}[/math], which is the quotient field of [math]\mathbb{Z}[/math]. And [math]\mathbb{Z}[/math] is pretty damn special, which makes each of the above pretty special.
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>>7769393
>>7769413

Physicists believe they know why complex numbers are useful because they see some quite interesting applications in their study. Nothing could be further from the truth and you should feel very bad for your arrogance. I would love to tell you a little about closed fields but I figure you're not entitled to such a serious answer. After all, you're justifying the existence of a set of numbers just by saying "but it's useful in this complicated theory!" so yeah although your comments are entertaining and gave me a good laugh, I believe that your limited knowledge about math is preventing you from knowing more.
This is what you chose, stupid physicist, when you decided you'd be settled with understanding how nature works, blissfully unaware of the existence of much greater things. And for that reason I will always laugh at your lack of curiosity.

Now tell me I'm an elitist, or autist, or whatever you people call mathematics students. I don't care. You're not even in a place where you could understand my point of view, so your opinion is immediately discarded. You normies amuse me.
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>>7769695
I haven't posted in this thread before, but if you say shit like

>This is what you chose, stupid physicist
or
>And for that reason I will always laugh at your lack of curiosity.

then I'd say it's justified to think "autist" when reading your post.
Imagine you're that guy and someone verbalizes something like "I laugh at you" ... this is straight out of some drama movie.
c'mon!

I also don't disagree with that guy that it can "just" seen as efficiency issue ... even if it is in fact the algebraic closure of the reals. The point he'd maybe like to make is how C has some nice representation in the invertible 2x2 matrices and so you could always reformulate shit without them - except we won't because it's more convenient with the use of i (and not think of it as {{0,-1},{1,0}})

>>7769684
you could say Z is the initial object in the category of rings.
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>>7769695
Math student here, you're fucking autistic.
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>>7763813
depends on the axiomatic system you're verifying your statements with
>>
>ln 5 isn't a constant
It turned out to be an honest mistake.

>>7763783
>At what level do my math and science teachers stop lying to me?
University level, I guess.
>>
>>7763813
if you were to travel north(i.e. at a right angle from east or west) from los angeles and another person traveled north from rome you would both eventually meet at the north pole.
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>>7769709
That's one reason [math]\mathbb{Z}[/math] is special, but there is something far greater about it.

[math]\mathbb{Z}[/math] is the least ring extending [math]\mathbb{N}[/math], and [math]\mathbb{N}[/math] (endowed with [math]+[/math] and [math]\cdot[/math]) is the most special object in all of mathematics.

[math]\mathbb{N}[/math] is, in an extremely strong sense, the foundation of all mathematics, and it is possible to regard [math]\mathbb{N}[/math] as the -only- mathematical object (!), in the following sense.

As first-order language is defined by induction on [math]\mathbb{N}[/math], it precedes set theory itself. First-order language, together with its operations, can be simulated in [math]\mathbb{N}[/math] — in this respect we can regard [math]\mathbb{N}[/math] as both a language and a structure, and that language-structure is a model over itself. And we don't need the nebulous notion of "set" to do mathematics — choose your favorite axiomatization [math]T[/math] of set theory, and the proof of Gödel's completeness theorem generates a definable imaginary substructure (i.e. the image of a model-theoretic translation) [math]\mathfrak{M}[/math] of [math]\mathbb{N}[/math] that models [math]T[/math], within which we can do all of mathematics.

There is only [math]\mathbb{N}[/math].
>>
>Parallel lines never cross


but parallel geodesics in hyperbolic geometry do not intersect either. And in spherical geometry there are no parallel lines. In what geometry do parallel lines intersect? Because I don't think they ever do.
>>
>>7770716
projective geometry
>>
>>7763783
>what are you on about?
>yes, four BASIC operations (really only two, at that)
>I doubt any teacher ever who was teaching you real math and not just "you're in 3rd grade, let me throw information at you you won't remember anyways and are going to need to relearn next year"
>In the real number system
>in Euclidean space
>>
>>7763783

They're just unstated assumptions.

>>There are no numbers less than zero
True assuming you're using the natural number system.

>>There are four operations: add, subtract, multiply, divide
True assuming that you insist on using only the standard arithmetic operators that have closure in the rational number system.

>>You can't divide all numbers evenly
True assuming you're using the integer number system.

>>Negative numbers don't have square roots
True assuming you're using the real number system.

>>Parallel lines never cross
True assuming you're using Euclidean geometry.

etc., etc.

If you want to claim that teachers who have unstated assumptions are "sloppy", then so be it. But people are sloppy about math in the real world too, so students need to get used to sloppiness. Sloppy teachers are doing them a favor.
>>
>>7764015
-([math]i^2 [/math])=1
>>
>>7764033
We don't do geometry on cones or spheres in high school.
>>
>>7764342
Lolwut, anon?
>>
>>7764060
>gnome has a silent g?

It depends.

The english word has a silent g.

For the Linux desktop, pronounce the g.
>>
>>7768808
>sum of all positive integers is -1/12
What?
>>
>>7770736
Three, exponentiation is it's own thing.
>>
>>7770818
Again, basic functions, like pre 4th grade
>>
>>7770826
I know, I didn't include derivation or integration or anything like that.
>>
>>7770222
>curves on a sphere
>lines
>>
>>7768113
Not in math, fucker.
>>
>>7770786
It's Ramanujam sum (not to be confused with its actual sum) is [math]-\frac{1}{12}[/math]. https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF

It's also a /sci/ meme.
>>
>>7770786

http://www.wolframalpha.com/input/?i=riemann+zeta+function+of+-1
>>
This thread was last in the catalog. Finally it can die.
>>
>>7770872
but with respect to science...yes.
>>
>>7763817
But anon, infinity isn't part of the numerical straight right? Is not a point, you never would reach infinity, therefore two parallel lines would never touch
>>
>>7768083
True... such over reactions like that person is what contributes to a culture "not wanting to be wrong' .. instead of "not caring if you are wrong"... Ok so now you know how to pronounce gnome properly... but that critic actually took the time to upload a gif and make fun of you... Yet, I recall the great scientist Feynman stating that when he discussed theories with class mates at university he often mispronounced them because he only read the name and didn't hear it's proper pronunciation.

People are so starved for the feel of being superior to others that they OVER react when they find a mistake instead of saying "No it's a silent g," they make endless noise about your small mistake. Not simply correcting and moving on without emotion is optimal.. where the correction with jest is something many low intelligent people often do.

As an experiment the next time you are around low IQ minorities or some group... mispronounce a common word then claim ignorance... They will laugh endlessly ...
>>
>>7763783
>>Negative numbers don't have square roots
They do?
>>
>>7768527
In a topos, truth values can be quite complicated.
For example, in the topos of sheaves on a topological space the truth values are the open sets of the space.
That's what I had in mind, since it seems to be the most general formalism that is studied by large numbers of people that has this property.
>>
>>7776046
No. i isn't the square root of -1 because sqrt(-1)^2=sqrt(-1*-1)=sqrt(1)
Op is a faggot
>>
>>7763783
Paradigms my fellow frogposter
>>
>>7776046
They do, it is called imaginary numbers. Come on now, even in HS they teach this.
>>
>>7768814
since mathematics at that level has such little connection to reality it doesnt require real dollars to do anything with it
>>
>>7764016
>If they say it's impossible to subtract bigger number from the smaller one
They weren't lying, they were just implicitly working only with the set of reals larger or equal to zero.
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