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i have this (decreasing) nested sequence of open sets (intervals of infinitesimal radius) about 0.

i just want to know if the intersection of the sets described above is still bounded away from 0.

that is, is it true that the countable intersection of such balls with infinitesimal radius will not be just the singleton.

i failed to prove that, with saturation, and i researched, there was sth with *R having uncountable cofinality, (every countable set is bounded)

i just need help understanding this.

thank you.

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# Non standard analysis

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