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.

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[–] EffortPostMcGee@hexbear.net 2 points 4 months ago (1 children)

I'm not really confused about what you're saying here exactly, and since the original post is deleted, I can't really even see what was originally said, but I was confused about this:

(like the real number that that sequence converges to given the standard topology of the space of real numbers).

Why make mention of the standard topology here exactly? It's not exactly clear to me why this has anything to do with what you two are discussing.

[–] Tomorrow_Farewell@hexbear.net 5 points 4 months ago (1 children)

Just to be specific, as what a particular sequence converges to depends on the topology of the space where we are looking for a limit of the sequence. Hell, in non-Hausdorff spaces a sequence can have multiple limits (trivial case: anti-discrete space of cardinality greater than 1 will have every sequence converge to every point in it).

[–] EffortPostMcGee@hexbear.net 4 points 4 months ago

Thanks for the clarification! In my mind, I sort of just think "metric first" so the topology induced by that metric is always just assumed, but that's because I don't ever work with non-metrizable spaces.