Help me argue that of a sequence x goes to limit l then

The negative sequence -x goes to the negative limit -l


Will pay if it's good

This post was edited by brigadier on Oct 29 2014 11:37am

Can you rewrite this question exactly as it is/was presented to you in your textbook or by your professor?

Assume that the sequence x converges to l. Then there exists an epsilon > 0 and n in N (where N is the set of all natural numbers) such that |x-l| < epsilon for all n >= N.
Then |x-l| < epsilon ==> l - epsilon < x < l +epsilon ==> epsilon - l < -x < -epsilon - l ==> |-x + l| < epsilon for all n>= N.
Therefore, by definition of convergence, the sequence -x must converge to -l.

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This post was edited by JDota72 on Oct 29 2014 12:13pm