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/sci/ - Science & Math

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7648132 No.7648132[DELETED]  [Reply] [Original]

>0!=1
>0.9999....=1
>1+2+3+4+5....=-1/12
Why are mathematicians so full of shit?
Why do we continue funding and respecting this sham of a field?

>> No.7648137

we dont fund them, they just stay in academic institutions like parasites

>> No.7648201

Literally a meme school of thought

>> No.7648210

>>7648132

The first is a convention. Factorial is only a meaningful operation in natural numbers, but when we see it in a sum which starts from zero but would have 0! in it to fuck up the first term, most agree it's useful to make it one so we don't need special cases.

The second is an artifact of base ten number systems. In base two, 0.101010... Is decimal 1/10: division just isn't always clean, and we can't help that. At any rate, the proof is trivial if you need convincing:

1/3 = 0.3333... , so mult. by 3:
1=0.9999...

The last one is a result which comes from using nonstandard mathematical sum manipulations. 1+2+...+n diverges as you would expect to plus infinity.

Lay off us mathematicians, we've done nothing wrong.

>> No.7648224

>>7648210
Wow, this thread looked like bait shitopsting but I actually learned something about maths

>> No.7648227 [DELETED] 

>>7648210
Watching numberphile shit while being in highschool doesn't make you a mathematician, though you might be just as bad.

>> No.7648229

>>7648210
>The last one
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF#/media/File:Sum1234Summary.svg

>> No.7648232

>list a few unintuitive results
>call field bullshit
Ive seen this bait before.

>> No.7648233

>>7648227
being a snarky shitposter won't make you right

>> No.7648373

>>7648210
does this mean there is no isomorphism between the decimal and fractional notations of the rational numbers? Or are such statements not equivalent?

>> No.7648376

>>7648373

Well there's no natural bijection since some fractions have two decimal notations.

>> No.7648385
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7648385

pic related

>> No.7648391 [DELETED] 

>>7648376
Like which? I'm thinking of non simplified fractions like 1/2, 2/4, 4/8 etc, of which there's a lot more than two.

>> No.7648453

>>7648132
>0!=1

How many ways are there to orient 0 things? It makes intuitive sense that it's 1. It also makes it so anything factorial isn't 0.

>.9999...=1

This is a result of a base 10 number system. If we used base 12 or another base with a lot of factors, this wouldn't happen.

1/3 * 3 = 1
.3333... * 3 = 1
.9999... = 1

The idea is that you never reach the last 9, so the number is functionally identical to 1. No matter where you cut off number, there will always be an infinite amount of 9s you didn't take into account.

>-1/12 meme

Numberphile can be cool and all, but please try to do some learning for yourself. It's a lot more satisfying to discover these things for yourself.

Math gets a lot more interesting when you realize that there are infinitely many conventions and axioms just waiting to be created. You don't have to use current conventions if you don't like them, you don't have to use them. You can just make up your own, assuming the logic makes sense (I'm talking about working in a different base and noticing patterns or coming up with limits and working with infinitesimals, not just making up random things that make no sense).

>> No.7648468

>>7648132
Ah yes OP, don't forget Gabriel's Horn.
>there exists an object such that the graph of (1/x) rotated around the x axis from 1 to infinity will yield an object with a finite volume but an infinite surface area.

>> No.7648502

>>7648453
What is the "-1/12" meme?
Do you need to be good at math to understand?

>> No.7648554

dont forget Banach–Tarski paradox

>> No.7648558

>>7648210
>1/3 = 0.3333... , so mult. by 3:
>1=0.9999.
That's not a proof. That's a failure of the notation to accurately represent the results of the underlying system. It's also inherent quantization error, or waiting to mask it.

>> No.7648579

>>7648502
>what is the -1/12 meme?
in fact, 1+2+3+4+5+6+7... "is equal to" -1/12
and that's fun because 1+2+3+4+5.. ->infinity
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF

>> No.7648607

>>7648558
>quantization error
No, it's not. Rational numbers don't have unique decimal representations. Deal with it.

>> No.7648625

>>7648132

Isn't the increasing factor phi and thats that?

>> No.7648629

>>7648607
Clearly they do if any instant of .9 repeating can also represent the next integer.

>> No.7648630

>>7648629
instance*

>> No.7648828

>>7648607

The earlier poster, who is not me, is however correct that your manipulation is not a proof, because its first line [amounts to] assuming what is to be proved, which is clear by taking it backwards. You might as well have arbitrarily started out with 1/10 = 0.0999... or anyplace else.

You could probably establish an iff statement between your two things, once you establish whatever ... means, but I can't be fussed and after all such a result still admits of the possibility where both equations are false (this is a hint to you).

What's actually needed is to state a clear definition of whatever ... means, and to perform a reductio ad absurdum banishing ritual with regard to the concept of an infinitesimal, where standard analysis is concerned. And no, I don't to hear about "b-but muh hyperreals" or similar, when you have to learn to crawl first.

t. math major