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Is this a bad definition of the rationals?
Considers (-2/-1) since -1 does not belong the the natural numbers, (-2/-1) would not be a rational number and I suppose it would be irrational if we define irrational as the complement set of the rationals.
Still we know that (-2/-1) and (2/1) are the same number and (2/1) is a rational number.
So this number both is and is not a rational number?
Am I the only one that thinks this is a paradox?
Is this definition of the rational common in textbooks? I usually see it defined when both numerator and denominator are integers.
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>>7942229
>Am I the only one that thinks this is a paradox?
>paradox
Yes, you are.
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>>7942234
Oh interesting, how would you define a paradox and why would this not be one?
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i think it's just referring to the fact that negative quotients -(n/z) are usually thought of as having a negative numerator (-n/z) even though this is purely a formality
Anonymous
What is the your favorite/most interesting geologic time period? 2016-03-19 06:51:06 Post No.7942046
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What is the your favorite/most interesting geologic time period? 2016-03-19 06:51:06 Post No.7942046
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What is the your favorite/most interesting geologic time period?
Anonymous
2016-03-19 06:51:06
Post No. 7942046
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Mine is the permian. The therapsids and amphibians are the most interesting creatures to me.
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post more ancient creatures
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>>7942056
ur mom
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>>7942046
Cambrian Radiation most exciting
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What if a parent universe had a black hole that sucks in matter, forming a white hole?
If so it'd explain the big bang and this general expansion of the universe.
This also ties in with the theory that black holes evaporate
Is the universe we know evaporating?
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'White holes' would violate even more laws of physics than black holes. Entrophy and thermodynamics are pretty well establlished and whiteholes would shit all over that.
The universe would be some gay shit with teleporting neutrons everywhere. Fucking dumb.
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>>7941878
White hole being a term for what we perceive as the big bang.
>Mass enters black hole
>Eventually releases matter
>Big bang
>Entropy
>Black hole evaporates entirely
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>>7941890
Just stop.
Trying to teach myself calculus. Explain to me why I can't find the area under this hyperbola, length of the thing, what not, using the perpendiculars that I spent 5 hours in Desmos doing addition of 1/sqrt(2) and 4/sqrt(5) and a bunch of other shit.
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>>7941695
because you'll be approximating the segments of the curve as straight lines?
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>>7941698
Then what is this meme staircase method I keep seeing? Is that only for repeating series? Define things, please?
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>>7941695
what's the curve's ecuation?
All you hear in undergrad is
>DON'T EAT OR DRINK IN THE LAB
>DON'T EAT OR DRINK IN THE LAB
>DON'T EAT OR DRINK IN THE LAB
At what level can I have a bottle of water or a cup of tea in the lab? What's wrong with having a snack while I'm babysitting some boring reflux reaction?
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because if you get to eat/drink in the lab others will too and its going to snowball into an accident
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>>7941653
>actually bringing food or drink into the lab
It's like you're asking to get poisoned. God knows what someone might slip into your drink or what might end up in your drink by accident.
I seriously can't believe there are people as stupid as you on attending university right now.
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Are you a flawless, perfect God who never makes a mistake, ever?
No? Then don't eat or drink in a lab. You're going to fuck up one day when you're tired or distracted and spill a drop of toxin into your tea or get a drop of supervirus on your BLT and fucking die
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w2c Rudin's or Tao's textbook on Analysis? Fucking hell shit can be expensive
pic obviously unrelated
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>>7941604
Just download the books.
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>Rudin
Literally pointless to use.
>Taos
Nobody has ever heard of it.
Both belong in the trash.
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Yeah, no way I'm paying 20 bucks for a brand new edition!
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So I'm reading through Zakon's Basic Concepts of Mathematics, and during the set theory introduction, we're asked to prove the basic operations of sets.
I'm coming directly from euclidean geometry, and I feel like this book does not present its definitions and axioms clearly enough. For example I have found out these proofs rely on basic laws of logic, e.g. the proof for the commutative law for sets is just the commutative law for logic, under a new name. That feels really silly. Is there a proof for this law in logic, or is it taken as an axiom?
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I believe most of those logical laws are proven by writing out the truth tables for the statements to be compared and if they are identical, that indicates equality. For example, writing the tables for A^(B || C) and (A^B) || (A^C) would yield the same thing.
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>>7941218
So the truth table for A v B would be:
A B AvB
T T T
T F T
F T T
F F T
whilst for BvA it would be
A B BvA
T T T
T F T
F T T
F F F
and this implies equality?
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>>7941286
Sorry, last one there should be F for the the first table.
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say somebody hasn't taken maths in a few years and they have 6 weeks to study until they start calc 1. what are the essentials that they should review?
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buimo
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>>7941059
>6 weeks to study
>calc 1
You litearlly have to do nothing.
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>>7941102
I wanna be prepared anonymoose
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Physics majors,
I understand that gravity deforms the spacetime through which it acts. In other words its presence changes the domain of its own propagation. What sort of mathematics do you guys use to represent that sort of thing where the solution to the problem changes the domain of the problem itself?
I'm trying to gain a more intuitive understanding of a solid mechanics problem in engineering, where stresses acting through a solid body deform the shape of the solid, further changing how the stresses act through the body. Over here we use some wonky PDE discretization techniques known as the finite element method, but I'm curious about how you guys go about solving similar problems to this.
t. mechanical engineering major
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>>7940124
>What sort of mathematics do you guys use to represent that sort of thing where the solution to the problem changes the domain of the problem itself?
pde
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>>7940124
>I understand that gravity deforms the spacetime through which it acts. In other words its presence changes the domain of its own propagation. What sort of mathematics do you guys use to represent that sort of thing where the solution to the problem changes the domain of the problem itself?
The wording of your question is weird and not really true. Gravity IS the deformation of spacetime.
To represent this we use what we always use. The principle of least action, which uses the calculus of variation to get Euler-Lagrange equations. The only difference is that now we're using the action S for spacetime itself instead of for an object moving through spacetime.
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>>7940124
In general relativity spacetime is described by differential geometry - specifically (pseudo-)Riemannian geometry. Differential geometry describes geometric spaces called differential manifolds, such as smooth curves and surfaces, and their higher dimensional generalisations. The specific details of distances and angles in this space are given by a metric tensor on the space, from which properties like the distance between points or the curvature can be derived - this is Riemannian geometry.
The mathematics of Riemannian geometry is usually (in physics, at least) described by tensor calculus, which you might be familiar with. A tensor is like a higher dimensional version of a vector, so a rank 0 tensor is a scalar, rank 1 is a vector, rank 2 can be represented by matrices etc. The metric tensor isn't actually a tensor, but a tensor field i.e a matrix at every point in spacetime. The Riemann curvature tensor is a rank 4 tensor field.
In GR, you either impose conditions on the metric using the Einstein field equations, or using the action principle that >>7940135 mentioned, which is also defined in terms of tensors. You can view the Einstein equations as a system of 10 PDEs, but the geometric interpretation in terms of tensors means you can apply all these geometric and topological techniques. The situation in electromagnetism was similar - Maxwell's equations were originally 20 differential equations in 14
(scalar) variables or something like that, but it reduces to 4 equations in 4 (vector) variables, which also emphasises the geometrical interpretation of E&B as vector fields on space. In GR we reduce 10 PDEs to 1 tensor equation, which also has a nice geometrical interpretation as matter causing spacetime to deviate from flatness. You could also apply tensor calculus to EM to reduce Maxwell's equations to 2 tensor equations, combining the E&B fields into one tensor field called the field strength tensor. This also has a geometrical interpretation.
Hello, /sci/. I would like to create a Facebook page dedicated to non-fiction books ratings. I need to gather a team of people interested in science who have some free time for reading and writing the ratings. Is anybody interested I. That kind of stuff?
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*in that
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>>7939981
How much will you pay?
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>>7940029
Ahaha. I will pay you nothing. It just would be joyful for you to gain your knowledge and share it with other people.
Anonymous
God Tier Engineering -- Part 2 2016-03-18 04:27:41 Post No.7939852
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God Tier Engineering -- Part 2 2016-03-18 04:27:41 Post No.7939852
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God Tier Engineering -- Part 2
Anonymous
2016-03-18 04:27:41
Post No. 7939852
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The Airbus A380, the world's largest passenger airline. Name your favorite engineering marvel anon.
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>>7939852
muh dick
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Falkirk Wheel.
https://www.youtube.com/watch?v=_tBH9SE-Kw8
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>>7939852
Just saw a documentary about hypercars. Pretty sexy senpai.
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What will happen to us when the magnetic fields flip? Will there be any danger?
Do we know exactly when the next time it'll flip is?
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just be thankful we still have a magnetic field
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Magnet based compasses will be messed up. Animal migrating birds might have trouble, assuming they actually use it.
But it's not like it's going to happen overnight. It'll probably take years to complete. Maybe even decades.
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>>7939756
I think its any time from now to the next 200,000 years. That bein said it doesn't just flip at one moment and it takes thousands of years to flip and it flips in zones first meaning there's not a period without a field.
Anonymous
Stupid Questions Thread 2016-03-14 00:39:43 Post No.7930606
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Stupid Questions Thread 2016-03-14 00:39:43 Post No.7930606
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Stupid Questions Thread
>How many joules of heat are needed to change 50.0 grams of ice at -15.0 degrees celsius to steam at 120.0 degrees celsius?
I fucking missed this and now I'm lost. I'm supposed to use these equations multiple times or something:
[math]q=mC\DeltaT[/math]
[math]q=n\Delta H_{fusion or vapor}[/math]
What's the difference between these equations and what do I actually do with them?
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>>7930606
fucked up the equation, it's
[math]q=mC \Delta T[/math]
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>>7930606
energy needed to raise heat up to 120 degrees.
plus energy needed to change ice to vapour.
state changes cost energy.
increasing the temperature costs energy.
so you need to use both.
my chem is a bit rusty, but its 4.2x135 + whatever the vapour value is for ice.
sorry. high school chem was like 5 years ago.
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Should I take all mineral supplements at once or at separate times of the day?
Will they compete for absorption if taken at once?
I'm currently using magnesium, zinc, copper, manganese, selenium and iodine. What should I add?
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>get put into two prerequisite 100-level courses (maths and physics) that I've already learned everything for because the NCEA examination system is bullshit and screws over people randomly
>university is completely unsympathetic even though it makes my degree a year longer and they acknowledge that I'm learning nothing, and they say "anon, if you know everything you should be able to get an A easily!"
>I actually end up being handicapped because I forgot how to do things like a begineer, such as calculating instantaneous velocity with limits rather than integration, or correctly interpreting physics questions made for physics beginners
>just end up getting slightly depressed whenever I do any university stuff physics or math related, doing the bare minimum
>except when I got annoyed because the physics course tried teaching me something that didn't make sense and later study on my own showed to be wrong
How can I survive this bullshit?
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>>7939224
I had the opposite problem:
>Start a masters
>Don't meet the pre-requisites for 2/3 of my electives.
>Boss the shit out of all of them, except algebraic geometry.
>Algebraic geometry is hard.
I've no idea how you survive your problem, I just put in a shit load of extra effort.
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>>7939229
Algebraic geometry reminds me of how shitty the rest of my course is.
So this trimester I'm taking:
MATH 141 (Calculus basics, already learned but abstracted from what I know)
PHYS 131 (Various physics, in the same form that I already learned so I could do last year's final examination with twice the pass mark easily)
MATH 151 (Really complicated algebra stuff, the lecturer knows his stuff but is incompetent as a teacher so I'm completely lost, I think it's algebraic geometry?)
COMP 112 (Tries teaching me good programming habits I already know, then hands me Java assignments that are hard because I have to learn how to translate my skills into Java)
Why does the only course that could be teaching me anything, MATH 151, have to also have the worst lecturer?
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These easy As work themselves out when you go to apply for internships with 4.0 gpa. They work out when it's year 4 and physics 9999 is kicking your ass.
Regards,
CC transfer who got thrown into the gpa killer classes his first semester
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Do you think the universe is finite or infinite?
I think the universe is finite because if it were infinite, there would be infinite copies of me, infinite copies of earth, and infinite copies of the observable universe, as well as other things not in our observable universe and then some.
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I believe that the universe is so large that it is irrelevant whether or not it is infinite.
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>>7938906
Look up in the sky at night... If any part of they sky is black then you have your answer
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>>7938906
I'd hope the universe is infinite so there's a version of you that's a little smarter.