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/sci/ - Science & Math

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4526719 No.4526719 [Reply] [Original]

When addition and multiplication of natural numbers are introduced in elementary school, why do the teachers just tell us to memorize them?
Why don't they show us how to derive them from the Peano axioms?

>> No.4526726

Give me any kind of mathematics you think you know, and we will give you a generalization of your ideas.

In short, this happens because intuition should come before rigour, at any level of mathematical sophistication, even graduate.

>> No.4526730

>>4526726
>intuition should come before rigour
Nope. Intuition is a nice optional feature, but worthless without rigor. Mathematics is based on rigor.

>> No.4526735

what the fuck is bondburger?

>> No.4526738

>>4526730
>before rigor
not
>without rigor

>> No.4526744

>>4526738
"Before rigor" means "without rigor", because the rigor doesn't exist at this time.

>> No.4526750

>>4526738
Don't argue with him, hes stubborn, unintelligent, and likely trolling.

>> No.4526755

>>4526750
Stubborn? Yes. Unintelligent? No.
And most importantly I'm right. It's mathematics. Truth is objective here.

>> No.4526756

>>4526744
"without" suggests there will never be rigor.

mathematicians, and math students, often use intuition and then apply rigor retrospectively. this may well fail, but it's still a very productive method.

>> No.4526760

Wittgenstein's Ladder.

>> No.4526762

>>4526755
as usual, you are right about everything when we translate you, but are using a version of english no one else uses, such as.

before = without

>> No.4526769

>>4526756
>"without" suggests there will never be rigor.
No, it means there currently is no rigor. No implications about the future are made.
If you read OP's post, you'd see that the problem is that children in elementary school are corrupted by being taught to value intuition higher than rigor.

>>4526762
I am using the English language my words are usually unambiguous.

>> No.4526774

>>4526760
Not really. I would claim that basic notions of mathematics such as addition and subtraction "exist", especially as they are inspired and derived from real world phenomena, independently of any specific formal construction or axiomatic system. It would be silly to teach peano axioms to elementary schoolers not only because they are too abstract and unnecessary for what most kids will do with math, but because it gives the impression that "this is the way things are" which is not entirely accurate.

>> No.4526782
File: 250 KB, 379x304, Reaction_Face_ASR_happy_win.png [View same] [iqdb] [saucenao] [google]
4526782

>>4526760
oh, nice. I just read the paragraph in tractatus 1h ago. I didn't know that statement made into a expression.

>> No.4526785

>>4526756
Obviously he is not a mathematician, neither professional or "at heart".

You think Euler derived his formula for perfect numbers out of this 'rigor'? Galois could've did what he did by rigorously studying the assumptions of people before him? No. Intuition is vital in mathematics.

>> No.4526783

Someone explain OPs pic.

>> No.4526787

>>4526785
I never said intuition is useless. But without rigor it's not mathematics.

>> No.4526790

>>4526769
>yawn

>> No.4526795

>>4526790
If you're tired, go to bed.

>> No.4526796

>>4526795
AWW SHIT, FKN REKT

>> No.4526802

>>4526783
That's the joke.

>> No.4526808

>>4526787
you said it was optional, yet its use is, so far as i can tell, universal

>> No.4526814

>>4526808
So? How does that affect my statement?
Intuition is optional. It might be helpful, but it isn't necessary. Rigor on the other hand is essential to all of mathematics.

>> No.4526820

Last night I double pounded your sister?

>> No.4526821

Ignore IQ fundie until he answers this:
>>4526779

>> No.4526832

Last night I daltonwhopper your sister?

>> No.4526835

>>4526814
Sure, rigor can be enough for derivative work. Develop your intuition for a chance at ground-breaking ideas.

>> No.4526837

>>4526821
I'm not gonna accept any of your inane challenges.

>>4526835
I agree.

>> No.4526841

>>4526837
>inane
Its completely relevant. You cannot claim to know what is important in mathematics if you don't know any mathematics. Answer it.

>> No.4526860

>>4526841
What "knowing mathematics" means is subjective. Your challenge is inane and trollish, because whatever answer I would give, you could easily dismiss it as too low level.

>> No.4526871

>>4526860
you could do it anyway

>> No.4526873

>>4526871
Why should I? My person is not relevant to the correctness of my posts.

>> No.4526876

>>4526873
could, not should

why not?

>> No.4526878

Pic is a troll; you'll spend hours trying to figure out the meaning, but there isn't any.

>> No.4526880

>>4526876
Because this is the science and math board. We deal with science and math here, not with persons.

>> No.4526881

>>4526873

that is the equivalent of saying that the machinery is not equivalent to what it produces; that the end justifies the means.

>> No.4526883

>>4526860
I would be satisfied with any knowledge above basic analysis/algebra definitions. Do you know the fundamental group? What a tensor product is? Can you apply the Sylow theorems?

There, now you have a few set goalposts.

>> No.4526888

>>4526881
Wrong. Truth in mathematics is objective and independent of the person posting it.

>>4526883
These are very specific questions. Are you trying to challenge me into doing your homework?

>> No.4526895

>>4526888
They are specific questions about important and basic concepts. You don't need to answer any of them specifically, but should show knowledge of approximately that level.

>> No.4526905

>>4526895
How should I "show" my knowledge? If I said I am familiar with the concepts you mentioned, you woiuld demand a proof. That means I had to accept any kind of challenge that either consists of doing your homework or results in you trolling me.

>> No.4526913

>>4526905
If "doing my homework" is what it takes then do it. Engage in the discussion instead of just trying to deflect everything that you can't win against.

>> No.4526915

ITT an annoying tripfag troll gets owned.

Also what is OP's image supposed to be. I'm really bad at those.

>> No.4526918

>>4526913
Why should I engage in anything I cannot win? Are you trying to troll me?

>> No.4526916

>>4526905
i won't demand proof, i'm just curious

be interesting to talk actual math/science with you instead of about math/science

>> No.4526924

>>4526915
So far I didn't get owned. Neither do I intend to get owned.

>>4526916
This thread already has its topic. When there are threads on other math or science topics, I will participate as well.

>> No.4526926

>>4526918
Sorry. Engage if you can win. Admit defeat if you can't, rather than deflecting. Anyway, its pretty clear at this point that you don't know any actual math. Kinda sad, since I'm of the same opinion as this guy >>4526916

>> No.4526927

>>4526924
>I will participate as well.

i have never seen you do this, i look forward to being pleasantly surprised

>> No.4526931

>>4526926
If that's your troll trick, then you have won a priori. Your question never allowed any chance for me to not end up being called out for "not knowing any math".

>> No.4526937

>>4526931
I gave you specific goal posts. I can even give you a specific problem, here:
Show that <span class="math">\mathbb{Q} \otimes \mathbb{Q}[/spoiler] is isomorphic to a one dimensional vector space over <span class="math">\mathbb{Q}[/spoiler]. I can't prove it isn't my homework, but you can't claim I didn't set specific enough goalposts. If you would like a homework problem from another field of math, name a field and I'll pick one.

>> No.4526939

>>4526937
Sorry, <span class="math">\mathbb{Q} \otimes_\mathbb{Z} \mathbb{Q}[/spoiler]

>> No.4526940

Lets see if /sci/ can use elementary Sylow theory then..

Prove that if ord(G) = 15, then G is cyclic.
=========================
I noticed that the group generated by the element a such that ord(a) = 5 (Cauchy's theorem) must be a normal group, as [G:<a>] = 3 and 3 is the smallest prime dividing the order of G (this theorem is proved in every graduate and probably most undergraduate books). So we have a normal Sylow 5-group. Who will go on?

>> No.4526956

>>4526940
Two ways to proceed: One is to show the sylow 3 subgroup is also normal and then counting elements. The other is to show that the sylow-5 subgroup is centralized by the entire group, because the quotient by the centralizer of the sylow-5 subgroup gives a homomorphism to its automorphism group.

>> No.4526974

Last night I Pierced burger your sister?

...what

>> No.4527025

Looks like IQ fundie got owned, he still hasn't answered >>4526937.

>> No.4527033

>>4527025
As I said, I'm not gonna answer it. My ability to answer it is not relevant. My posts gain their truth not from me being any kind of authority, but from being mathematically correct.

>> No.4527044

>>4527033
How does mathematical correctness make sense in non-mathematical statements like all of yours are?
You are permanently talking about things that can only be known by people who have done mathematics for a while, and hence the only way your posts have any truth is precisely by authority.
Go ahead and answer the goddamn question, it's first-year stuff for fuck's sake.

>> No.4527049

>>4527044
I'm only talking about things that are objectively discussable. This requires no authority.

>> No.4527053
File: 73 KB, 400x541, 1323299170702.jpg [View same] [iqdb] [saucenao] [google]
4527053

dickwaving to the left, dickwaving to the right

>> No.4527110

Allright it's official: that tripfag has no idea of math.

>> No.4527118

last night I spyed on your sisters buns

>> No.4527119

>>4527110
Show me a post of mine that is incorrect. I dare you.

>> No.4527126

>>4526937
<span class="math">\mathbb{Q}\otimes_{\mathbb{Z}}\mathbb{Q}\cong\mathbb{Q}[/spoiler]

>> No.4527131

>>4527118
Definitely not bro, it's "Last night I James hamburger your sister".

>> No.4527133

>>4527126
Yes, that is what he was asked to prove.

>> No.4527134

>>4527119
Here you go: >>4526730.

When actually doing mathematics intuition should indeed come before rigor. But you wouldn't know of course since you don't actually do any math.

>> No.4527135

>>4527133
He was only asked to prove that it is isomorphic to a 1-dimensional vector space over Q. What I'm saying is that the tensor product is naturally isomorphic to Q. It's a stronger statement and the reason why the original statement is true.

>> No.4527139

>>4527135
Q *is* a one dimensional vector space over Q. The only difference is that calling it a vector space makes it explicit that you are talking about it as a module/vector space rather than a ring.

>> No.4527147

>>4527134
You do not contradict my post. Intuition can come before rigor, but wihout rigorously proving the results of your intuition, you are not allowed to call it mathematics.

>> No.4527150

>>4527147
>you are not allowed to call it mathematics.
According to what?

>> No.4527153

>>4527150
According to a special dictionary.

>> No.4527154

>>4527139
The key point of my post is the word "natural". Maybe I should've written what some author do:

<div class="math">\mathbb{Q}\otimes_{\mathbb{Z}}\mathbb{Q}=\mathbb{Q}</div>

Notice the equality instead of congruence sign. All I'm saying is that it's easier to see that the tensor product is naturally isomorphic to Q than to just show the original statement directly. So in a sense I'm giving away part of the proof.

>> No.4527159

>>4527150
So you are saying intuition alone is a mathematical proof? Then why did Perelman get any attention for proving rigorously what was intuitionally obvious?

>> No.4527160

>>4527154
Sure, I just disagree with your claim that that is "stronger" as, although that is a simpler way to describe it, the two statements are equivalent.

>> No.4527163

>>4527159
I never said proof. I just disagreed with the claim that intuition is not mathematics. You should think about your own posts more.

>> No.4527164

>>4527159
>changes "call it mathematics" to "call it mathematical proof"
>will then define "mathematics" as "proving mathematics"
>will then claim no circularity

>> No.4527172

>>4527163
The way how a person finds a solution is not important to mathematical truth. Only the proof counts. You can come up with a lot of bizarre intuition only you understand. No one cares. Either you can prove it or you can't.

>>4527164
Mathematics is all about proofs. Wild geussing wihout basis is at best philosophy.

>> No.4527178

>>4527172
I'll tell you what. I'll accept your definition of mathematics if you can prove that our axiom system is consistent. Good luck.