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.

  • Tomorrow_Farewell [any, they/them]
    ·
    6 months ago

    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 [any]
      ·
      6 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.