Browse Teach Curate

Sequences as Functions on the Natural Numbers in Real Analysis

A sequence of real numbers is a map from the natural numbers into the reals, written (a_n), not merely an informal list of values written out with dots. After learning this a student can read the notation (a_n) and say what its domain and codomain are, plot a sequence as a discrete set of points rather than a continuous curve, and distinguish the index n from the value a_n when reasoning about a claim made for all large n.

jeremy Video

The Epsilon-N Definition of Sequence Convergence in Real Analysis

This concept covers the epsilon-N (also written epsilon-capital-N) definition of convergence for a sequence of real numbers, part of real analysis: a sequence a_n converges to a limit L if, for every…