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Nov 12, 2012 14:57:20 GMT -6
Post by Damocles on Nov 12, 2012 14:57:20 GMT -6
Hi, I am trying to prove that [latex] \{n\}_{n\in \mathbb{N}} [/latex] does not converge (based on definition of convergence).
I can prove this by contradiction saying assume it converges, fix [latex] \epsilon [/latex] , then [latex] x_n < \epsilon + a [/latex] (for [latex] n \ge N [/latex] where N is fixed) (by fundamental theorem of ineq.) but by Archimedean Principle, I can find a natural number that surpasses this bound, i.e. [latex] \exists m , m x_n > \epsilon + a [/latex] which is an element of the sequence [latex]x_n[/latex] which means for some M, [latex] n \ge M \rightarrow x_n > \epsilon + a [/latex] which is a contradiction.
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Feb 4, 2013 13:51:48 GMT -6
Post by thepoubel on Feb 4, 2013 13:51:48 GMT -6
wat
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