2 replies on “Math From Scratch 31: Limits”

  1. I don’t know if you have used the Archimedean axiom for the reals: For any two positive reals x and y, there is an integer n such that n*x > y. This, combined with Bernoulli’s inequality ((1+x)^n >= 1 + nx) will allow you to show that lim_{n -> infinity} r^n = 0 for 0 < r < 1.

    I can provide more info if you want. email me at [email protected].

    • I’ve got it in my resources, but it isn’t strictly necessary to define the real number set so I haven’t used it yet. It’ll come up later.

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