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May 3, 2018 / porton

Expressing limits as implications

I have added to my book section “Expressing limits as implications”.

The main (easy to prove) theorem basically states that \lim_{x\to\alpha} f(x) = \beta when x\to\alpha implies f(x)\to\beta. Here x can be taken an arbitrary filter or just arbitrary ultrafilter.

The section also contains another, a little less obvious theorem. There is also a (seemingly easy) open problem there.

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