/sci/ - Science & Math

>>12692234
>tfw trying to count the number of partial orders on a 20-element set

>>9052815
>Finite systems just don't have the elaborate structure of infinite ones. Things get a lot messier.
You can (almost) always embed a finite system in an infinite one, so that's not really true in general.
I think it usually appears this way because we're unable to enumerate all infinite structures using a finite sequence of symbols (insert an appropriate diagonal argument here) so we restrict our attention to the infinite systems that can be described as being generated from a small number of rules. In which case the simplicity of the structure is merely reflecting the simplicity of the defining ruleset and can't really be generalized (if you could place a measure over the infinite structures, the "simple" ones would probably have measure 0).

>>8528965
>>8528979
>>8528996
Well shit, that didn't turn out to be as difficult as I expected.

Fine, here's another one:

A bag contains 10 balls labelled 1 to 10. I draw two balls from the bag and tell Albert the product of the two numbers drawn. I tell Bernard the (absolute value of the) difference between the two numbers, and I tell Cheryl the sum.

Immediately afterwards, the following conversation happens:
Albert: I don't know what the two numbers are.
Bernard: Neither do I.
Cheryl: Neither do I.
Albert: Now I know what they are.
Bernard: So do I.
Cheryl: So do I.

What are they?

>>8461346
Huh, you're right (albeit up to a constant factor of two in the denominator, so the result should be S/2). How did I miss that?

More importantly, does this make Wolfram Alpha infallible?

>mfw fixed-points can only be asserted to exist, or require infinitely many function applications
Is there a way of constructing fractals in terms of some kind of universal property?