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/sci/ - Science & Math

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2264792 No.2264792 [Reply] [Original]

If physicists are so much smarter than chemists, then why are they still stuck on hydrogen?

>> No.2264796

You know how if you take a sequence of integers, you'll reach any number you want eventually, but if take a sequence of irrational numbers, you'll never even get past one? It's kind of like that.

>> No.2264820

You'll never even get to the next algebraic number after 0.

>> No.2264825

>>2264792
Are you even a physicist? In some way? Little bit? ...
(And the answer is that your question is wrong.)

>>2264796
Are you even a physicist? In some way? Little bit? ...

GRRRRR

>> No.2264829

>>2264796
>if you take a sequence of integers
OK, I take the sequence, x_n = 1

>you'll reach any number you want eventually
nope

>> No.2264837

What about philosophy?

>> No.2264838

Silly, silly me, going out and opening my big mouth again....

>> No.2264839
File: 173 KB, 640x533, 1281936944685.jpg [View same] [iqdb] [saucenao] [google]
2264839

>>2264825
>>2264829

>> No.2264853
File: 238 KB, 469x492, 1293220220581.png [View same] [iqdb] [saucenao] [google]
2264853

>>2264839
THIS. This is the pic that I saw long ago and it inspired
>>2264796
Saving so that future references of such a nature are accurate.

>> No.2264856

>>2264839
Wow that is poorly written and even wrong.
There are an infinite number of infinities, not only 2.

>> No.2264875

>>2264856
Look, they're clearly referring to aleph-nought and aleph-one. I don't think it's necessarily precluding the existence of aleph-two etc.

>> No.2264887
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2264887

>>2264875
>aleph-nought
>aleph-one
>aleph-two
MFW I have never even heard of those terms before. It appears I still have much to learn.

>> No.2264912

>>2264887

Aleph is a funky N used to represent the cardinal number of the set of natural numbers (which is infinite).

Aleph-1,2, etc. represent higher orders of infinity.

>> No.2264955

>>2264839

The problem with this is that the Reals are so much more than "an infinity of infinities".

The Rationals are an infinity of infinities, but they are still countable.

>> No.2264959

>>2264912
using that notation is not very helpful. It has not been proven that there is no distinct cardinalities between the size of integers and the size of real numbers.

>> No.2264961

>>2264959

And it can't be. So why bother?

>> No.2265003

>>2264959
depends on what you are doing, no?
if you write down any two reals, there are always an infinite number of reals between them. not true for rationals or integers

>> No.2265032

>>2265003

It is true for Rationals. This is a misleading way of looking at countability.

>> No.2265036

>>2265003
That actually is always true for rationals.

I think you're missing my point though. The cardinality of the size of the set of real numbers in between any two distinct real numbers is the same as the cardinality of the set of ALL real numbers.

>> No.2265046

>>2265036

That also holds for Rationals.

>> No.2265050

>>2265032
I don't think we're talking about countability here. There are uncountable sets that are aleph-naught, and countable sets that are aleph-one

>> No.2265061

>>2265046
I didn't mention that because it was a digression from my original point that it hasn't been proven that there aren't cardinalities between aleph-nought and aleph-one

>> No.2265089

>>2265050

You sure about that? That seems like it would lead to a contradiction somewhere down the line.

>>2265061

And it can't be proven. The continuum hypothesis is independent of ZFC.

>> No.2265110

>>2265050
countable set
<span class="math"> \aleph_1 [/spoiler]

pick one

>> No.2265119

>>2265050
uncountable
<span class="math"> \aleph_0 [/spoiler]

pick one

>> No.2265142

Is there any site/pdf/paper out there that'll teach me about this aleph business at a very elementary level? It's times like this I kind of regret not taking math past calculus II.

>> No.2265882

>>2264959
i can prove you wrong, and it is actually very easy. but you've left, so there is no point.

>> No.2265898

>>2264796
This is one of the stupidest things I've ever read. And I've read a lot of stupid things.