Do all finite sets have a formula that, given n, will output

what do you mean by formula?

is there a formula for the set {square, circle}?

>>8994058
{a1,...,an}
f(i)=ai

>>8994058
of course. let X be a set with a finite cardinality k. let f be a bijection between {1,..,k} and X which exists by elementary set theory. then f(n) is your "formula".

{1,1,1,-3,20}
t(1)=1
t(2)=1
t(3)=1
t(4)=-3
t(5)=20
t(n)=?

You're looking for a equation that gives those desired outputs? Like f(i) = 25i - 3 or something like that?

>>8994076
>{1,1
Want to know how I know you're a retard?

File: maxresdefault.jpg (138KB, 1920x1080px) Image search: [Google]

138KB, 1920x1080px

>>8994507
>he doesn't use multisets

Does there exist a set S, where no possible function's domain covers ever element of S.

Is this what you mean? Or the inverse of what you mean?

>>8994058
if a formula, you mean some closed algebraic formula, then yes. look up polynomial interpolation

>>8994061
circle: x=cos a, y = sin a

>>8994496
You can do this thing I guess:
https://en.wikipedia.org/wiki/Polynomial_interpolation

>>8994058
>a formula
L0Lno fgt pls

>>8994058

not really

I beileve in the construction of the reals it's like "oh yeah and you can't do that for this set"

>>8994513
>>8994507

muh spectra