Real numbers and Cauchy sequences of rationals (III) | Real numbers and limits Math Foundations 113

[@adamwhiteson6866]

Despite having worked through Rudin's Real Analysis, this discussion clarified a lot of things for me.

[@FergalByrne]

It’s not just that the bounds are lost if you use the Cauchy sequence, you have now zero control or information about when in the future your N’s might start working. Having an I_k says all the future values lie in that range, you get full value for doing the work up to k.

[@twwc960]

Hi. Another great lecture. This is a very minor point, but something you might want to correct. On the first slide, near the bottom where you define equality of interval sequences, I think the prime should be on the I, not the k, in other words I think you mean to have "I prime sub k" rather than "I sub k prime".