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 Post subject: Sequence problemPosted: Fri, 11 Feb 2011 19:25:22 UTC
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Is there a monotonic increasing sequence such that ?

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 Post subject: Re: Sequence problemPosted: Fri, 11 Feb 2011 19:37:38 UTC
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Is there a monotonic increasing sequence such that ?

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 Post subject: Re: Sequence problemPosted: Fri, 11 Feb 2011 22:30:08 UTC
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robbwrr wrote:
Is there a monotonic increasing sequence such that ?

What if the indexing set is ?

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 Post subject: Re: Sequence problemPosted: Wed, 29 Feb 2012 17:16:05 UTC
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Is there a monotonic increasing sequence such that ?

Maybe I'm missing something, but would satisfy the conditions, as well as outermeasure's extension?

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 Post subject: Re: Sequence problemPosted: Wed, 29 Feb 2012 17:18:40 UTC
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DJJazzyDan wrote:
Is there a monotonic increasing sequence such that ?

Maybe I'm missing something, but would satisfy the conditions, as well as outermeasure's extension?

Monotone increasing.

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 Post subject: Re: Sequence problemPosted: Wed, 29 Feb 2012 19:31:18 UTC
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Monotone increasing.

My mistake, confused with nondecreasing.
Spoiler:
There cannot be such a sequence when the indexing set is
Proof: Consider there was such a sequence
Then for some , say 2
which implies
and
which implies

Since the sequence is monotone increasing, which is a contradiction.

There is a similar proof, I believe, by considering the index -2,-1, and 2

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