Wait what? (1+2+3+4+...

[BAndrew]

But how can something approach infinity, infinity is not a number it's a concept. Can you please explain from the very grounds up how exactly infinity can be used to calculate something, how is it defined (because it has to be in order to be used, otherwise it's just hocus pocus and make-believe) and how can you be so sure that the result is in fact true when a part of the calculation is undefined, that is, have no value?

What do you mean "how can something approach infinity"? Is there something that stops it from doing that? Infinity is an abstract concept describing something without any limit. What you are obviously confusing here is the limit of a function f with unboundedness of infinity. They are two completely different things. If the result wasn't true then how come there are areas (surfaces)? Surfaces consist of infinite points (size 0) and yet they have a certain area. Infinity is not a number, but a concept as you said, but I don't get your reasoning here. I don't treat it like a normal number, I just use it on a calculation.

No, no that it wasn't true before we "discovered" it, but that we didn't know it was applicable before we invented it.

Then if the theorem was true before we discovered it, it means that it was discovered and not invented.
Listen I don't know what's on your mind, but we don't invent everything.

We invent machines, computers, books, buildings, medicine, maps, tools, clothes, etc.

We don't invent theorems,electrons,particles,mathematical ideas,laws of physics and the universe. We discover them.