Recent content by mathkiddi

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    Nested intervals, uncountable sets, unique points.

    no, we have not covered compactness.
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    Nested intervals, uncountable sets, unique points.

    Homework Statement Let [a,b] be an interval and let A be a subset of [a,b] and suppose that A is an infinite set. Suppose that A is uncountable. Prove that there exists a point z which is an element of [a,b] such that A intersect I is uncountable for every open interval I that contains...
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    Prove a Cauchy Sequence using Geometric Sums

    Homework Statement Let {x_n} be a sequence. and let r be a real number 0<r<1. Suppose |x_(n+1) - x_n|<=r|x_n -x_(n-1)| for all n>1. Prove that {x_n} is Cauchy and hence convergent. Homework Equations if |r|<1 then the sequence \sum r^k from k=0 to n converges to 1/(1-r) The...