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cauchy sequence?
explain what a cauchy sequence and convergent sequence are and give an example of a cauchy sequency that does not converge
1 Answer
- WillLv 51 decade agoFavorite Answer
A Cauchy Sequence is a sequence which the terms get closer and closer together, ie. for all epison > 0, there exists an N on the naturals such that for n,m<n | x_n - x_m| < epsilon. A Convergent sequence just gets closer to a value. That is for all positive epsilon the exists an N on the naturals such that for all n>n |x_n - L| < epsilon, where L is what the sequence converges to.
An sequence in which the distance between the terms doesn't get strictly smaller is not cauchy. Like {1,2,3,4,5,6....}