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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?

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.

rvba 1y ago
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
- deleted 1y ago
  [deleted]
- croes 1y ago
  But that would mean (0/0) * 2 = 2 but (0/0) * (2/1) = (0 * 2) / (0 * 1) = 0/0 = 1
meroes 1y ago
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.
margalabargala 1y ago
> 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 1y ago
  https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B...
  - margalabargala 1y ago
    Well that's really fun! I had no idea, thank you.
- glacier5674 1y ago
  [dead]
- ForOldHack 1y ago
  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.
Affric 1y ago
> 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.

rvba 1y ago

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

deleted 1y ago
[deleted]
croes 1y ago
But that would mean (0/0) * 2 = 2 but (0/0) * (2/1) = (0 * 2) / (0 * 1) = 0/0 = 1

meroes 1y ago

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.

margalabargala 1y ago

> 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 1y ago
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B...
- margalabargala 1y ago
  Well that's really fun! I had no idea, thank you.
glacier5674 1y ago
[dead]
ForOldHack 1y ago
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.

Affric 1y ago

> 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.