Every Cauchy sequence is bounded.

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  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. calculus
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Комментарии
Автор

I remember this being exactly something i had to prove in my introductory analysis final exam. Good times lol

TrinoElrich
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If I walk in my math class and see shit like this I will implode

CardSeven
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shouldn't it be a lesser-or-equal in the last bit, i.e. 1 + |a_N| ≤ M? Or is there a reason why 1 + |a_N| can't be the maximum?

LDericher
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Inequality always leads to bias, then prejudice, and then, envy, ...and if there are 2 max's in the list, then war for supremacy. Of course cauchy knew all that and thought he could mediate, buuuutt, likely died before it could happen.

ruffifuffler
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Does this same proof generalize for cauchy sequences in a metric space?

nicholasroberts
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I would argue that this sequence is convergent with the limit a. So {a_n: n natural} has a comvergence point a. Every set with such a point is bounded so the sequence must be bounded as well.

wolframhuttermann
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Cauchy sequence - no idea what that is....

cpk