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Limit Inferior

Suppose a_n >0 for each n in N and lim inf (a_n) > 0. Prove there is a number a>0 st a_n >/= a for all n in N. (limit n--> infinity)

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Since b=lim inf(a_n)>0, then we can find some N>0, such that |inf(a_n)-b|<b/2 for all n>N. This implies that inf(a_n)>b/2 ...

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A limit inferior proof is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.