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<Regenaxer>
?/
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<freeemint_>
Hello i am in a metrical space where each cauchy sequence converges against a member of the space. There is a sequence (x_n) for which i proved: the |x_n-x_{n+1}| converges against 0. How do i show x_n converges?
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<freeemint_>
Sorry wrong chat ;D
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<Regenaxer>
rdd
<rick42>
freeemint_: curious: is that for a course? if so, what text are you using? we used kolmogorov-fomin, but that was back in the 90s :)
<rick42>
hi all
<rick42>
:)
<freeemint_>
rick42: This for a course it is called "Analysis 1"
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<miskatonic>
it is not sufficient to prove
<miskatonic>
the harmonical series diverges although |x_n-x_{n+1}| converges to zero
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<miskatonic>
as picolisp does not support floats, such a thing has no relevance for us
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