In this installment, we introduce limits and use them to lead to the notion of complete sets. This is the last piece we need to define real numbers next month.
In this installment, we introduce limits and use them to lead to the notion of complete sets. This is the last piece we need to define real numbers next month.
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.