[munchler]

Other good nerd-sniping math questions:

0^0 = 1? Yes, it’s simpler that way.

0! = 1? Yes, it’s simpler that way.

0/0 = ∞? No, it’s undefined.

0.9999… = 1? Yes, it’s just two ways of expressing the same number.

1+2+3+… = -1/12? No, but if it did have a finite value, that’s what it would be.

[Affric]

> 0.9999… = 1? Yes, it’s just two ways of expressing the same number.

More a question of place-value representation systems than what most people are thinking of which is 1 - ε.

[margalabargala]

> 1+2+3+… = -1/12? No, but if it did have a finite value, that’s what it would be.

The other ones, sure, but I'm not following this one.

[munchler]

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B...

[margalabargala]

Well that's really fun! I had no idea, thank you.

[ForOldHack]

You missed the lecture on the missuse of infinities.

If I have inf*k = inf,and dvide both sides by inf... ( The misuse) Then 1 = any K including 1/12. Now this is useless in calculus and number theory, but in quantium field theory it is a useful tool.

So inf = 1/12 and a non convergent series = a constant, but you have misused dividing infinity by itself to get it.

Infinity for division? It's useful, like counting chickens starting at zero. L'Hoptals rule is a very useful tool, but do not misuse it.

[rvba]

If we try to define division by zero, shouldnt 0/0 be 1?

Or even more abstract "every element on y". Which I think could sort of work

[croes]

But that would mean (0/0) * 2 = 2 but (0/0) * (2/1) = (0 * 2) / (0 * 1) = 0/0 = 1

[meroes]

0^0 got Gemini 2.5 pro the other day for me. It claimed all indeterminate forms (in the context of limits) are also undefined as a response to a prompt dividing by zero. 0^0 is the most obvious exception, it's typically defined as =1 as you said.