/math/ - Mathematics

this but axiom of choice is also bullshit

I bought once some English chips which turned out to be a package of packages in chips. Does it mean I can duplicate chips?

I think the validity of the use of the real numbers depends on whether space is continuous or discrete, or whatever it is. I don't know of a way to prove either or. But definitely the popular notation of Writing Real Numbers as Neverending Trailing Decimal expansions is quite pointless as those numbers can't be written in decimal. Same for some rational decimal expansions. Since you can't split something into 3 parts without a remainder if it is not already a multiple of 3. In decimal, the base isn't a multiple of 3 so if you divide 1 by 3, you should always have a remainder after the division. the unending length of 3s that is commonly used would never equal 1/3 as it would be impossible to write 1/3 using a decimal expansion because there is always a remainder as a result of that division.

>make imageboard to filter midwits
>it's somehow still filled with finitists

>>362
so that must mean finitists aren't midwits.

Why does mathematics have to be limited to the real world? To me this seems to be an underlying assumption for finitists.

>>299
You don't need AC for top though, just always choose the ball that isn't gray like the rest.

Infinites are real but we cannot access their forms directly. We only see the projections on the cave wall :)

>>299
Sorry, I haven't seen that notation for the last equation before, is that supposed to be axiom of infinity? Does y' represent successor? I've seen {y} U y and S(y).

>>709
it is, that notation is definitely nonstandard. Similar notation is y^+

>>710
Thanks
>>299
I mean, if ZFC still works without it, there could be an argument that it isn't 'real'. Could remove Infinity, Replacement, Choice, and I think Foundation.

>>543
Bizarre shit because while infinities aren't tangibly real, finite integers also aren't.

>>299
I have never understood diagonalisation argument.

i never understood why the diagonalization argument doesnt work with the natural numbers
you could consider all natural numbers to be sequences starting with the least significant digit
and then construct a sequence that differs along the diagonal and this sequence must be unique by construction

>>759
The problem is that one would need to restrict to eventually zero sequences, the sequence you'd construct however wouldn't be eventually zero.

>>712
Your post made me realize that being able to conceptualize abstractions that don't actually exist is what we learn to do as toddlers; finitists are essentially just stuck on the adult version of this leap. That's pretty funny.

>>604
Hello

>>299
ggggggggggg