The Bolzano Weierstrass Theorem states that every bounded sequence of real numbers has a convergent subsequence. It doesn’t matter how strange or random the sequence appears to be, as long as it is bounded then at least one part of it converges. This theorem, introduced by Karl Weierstrass in about 1840, was the first major result guaranteeing limits of sequences.
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Bolzano-Weierstrass teoremi
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