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Unformatted text preview: . (b) Every neighborhood of x contains innitely many points of S . (c) Every neighborhood of x contains a point of S that is dierent from x. (d) Every epsilon neighborhood of x contains a point of S that is dierent from x. 8. Bolzano-Weierstrass Theorem : Every bounded innite set of real numbers has at least one accu-mulation point. 9. Theorem : Every Cauchy sequence converges to real number. (This is equivalent to the completeness property of real numbers). 10. Subsequence . 11. Theorem Every bounded sequence has a convergent subsequence. 12. Increasing sequence. Decreasing sequence. Monotone sequence . 13. Theorem : Every bounded monotone sequence is convergent....
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This note was uploaded on 08/12/2009 for the course MAT 371 taught by Professor Thieme during the Spring '07 term at ASU.
- Spring '07