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Math Help - Cauchy sequence

  1. #1
    Junior Member platinumpimp68plus1's Avatar
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    Cauchy sequence

    Does anyone have a concrete example of a Cauchy sequence that is not convergent?
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  2. #2
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    Krizalid's Avatar
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    i remember i studied once these, and every Cauchy sequence is convergent.

    is there any counterexample, because i'm about to die.
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  3. #3
    Junior Member platinumpimp68plus1's Avatar
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    Quote Originally Posted by Krizalid View Post
    i remember i studied once these, and every Cauchy sequence is convergent.

    is there any counterexample, because i'm about to die.
    Every convergent series is Cauchy... but in general, the converse isn't true. Only in R.
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    oh, i'll have to review my notes.
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  5. #5
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    Quote Originally Posted by platinumpimp68plus1 View Post
    Does anyone have a concrete example of a Cauchy sequence that is not convergent?
    It all depends on which spaces you're working. For example in working with \mathbb{R} we have that x_n=\left( 1+\frac{1}{n} \right) ^n is convergent, but if you're in \mathbb{Q} this sequence is Cauchy but not convergent.
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