Can unfortunately confirm

I always eat ice cream with a spoon. I can’t stand any other form of it.

It can’t be shown to be equivalent to -1/12. The sum definitely just simply goes to infinity. However, if you use some specific nonstandard definitions, you can squeeze out -1/12.

What I think is interesting is how many choices of nonstandard definitions you can use to “prove” this result. I can recall 3 just right off the top of my head. However, as these are nonstandard definitions, one can’t really say that the sum is -1/12 without specifying which logical system you are operating in, because the default system makes it simply untrue.

It’s like saying that 2+2=0. Sure, you can define the + sign to be some nonstandard function, but unless I describe that function to you, I can’t just simply tell you 2+2=0, because you’d just assume the standard definition of +, in which 2+2 definitely isn’t 0.

I can’t claim it’s as high quality as the channels you’ve mentioned, but I actually have a channel! I only have one video at the moment, because they take a long time to make, but I’m planning on having the next one out perhaps within the next month.

https://m.youtube.com/@axiomath3434

That’s a really great question. The answer is that mathematicians keep their statements general when trying to prove things. Another commenter gave a bunch of examples as to different techniques a mathematician might use, but I think giving an example of a very simple general proof might make things more clear.

Say we wanted to prove that an even number plus 1 is an odd number. This is a fact that we all intuitively know is true, but how do we know it’s true? We haven’t tested every single even number in existence to see that itself plus 1 is odd, so how do we know it is true for all even numbers in existence?

The answer lies in the definitions for what is an even number and what is an odd number. We say that a number is even if it can be written in the form 2n, where n is some integer, and we say that a number is odd if it can be written as 2n+1. For any number in existence, we can tell if it’s even or odd by coming back to these formulas.

So let’s say we have some even number. Because we know it’s even, we know we can write it as 2n, where n is an integer. Adding 1 to it gives 2n+1. This is, by definition, an odd number. Because we didn’t restrict at the beginning which even number we started with, we proved the fact for all even numbers, in one fell swoop.