This little guy craves the light of knowledge and wants to know why 0.999… = 1. He wants rigour, but he does accept proofs starting with any sort of premise.
Enlighten him.
The ellipses mean infinity. Anything less than infinity and the equation is false. It looks unintuitive because infinity is unintuitive
The ellipses mean infinity
No, it does not. The ellipsis notation is used to denote a repeating pattern. It is not used to denote points that are named ‘infinity’ in spaces like Aleksandrov compactification and the extended space of real numbers.
I am sorry, but your reply lacks rigour.
Is this a bit? I meant that the ellipses, in this context, mean that the nines go on forever. Obviously there are other symbols used to represent similar ideas, like ∞
I’m being serious. The word ‘infinity’ refers to some points from spaces like Aleksandrov compactification. It does not refer to any sort of repetition of any pattern. You cannot, for example, write ‘0.999∞’ or ‘0.999infinity’ to mean the same thing as ‘0.999…’ or ‘0.(9)’.
