# Tag Info

### Prove, by nonstandard reasoning, that the limit superior of a sequence is a cluster point.

A natural approach to try would be to use the ideas around saturation/idealisation. With respect to the order relation, finding the maximum among the extended terms of the sequence is obviously ...
• 43.9k

### Prove, by nonstandard reasoning, that the limit superior of a sequence is a cluster point.

$\newcommand\ext{{}^*} \newcommand\N{\mathbb N} \newcommand\sh{\mathop{\mathrm{sh}}}$Let $\N_\infty = \ext\N\setminus\N$ and let $S = \{\sh(\ext s_\omega) \;:\; \omega \in \N_\infty\}$ be the set of ...
• 7,244
1 vote

### Prove, by nonstandard reasoning, that the limit superior of a sequence is a cluster point.

I couldn't quite reconcile my understanding of Goldblatt with the details provided in the other answers. Given my intense struggle over this same question and eventually figuring out a proof, I ...
• 389
1 vote

### intuition on lim sup and lim inf in probability spaces

The terminology "almost all" in this situation simply means all but finitely many (also said cofinitely many). It does not really have anything to do with the order structure of the natural ...
Accepted

• 2,967
1 vote
Accepted

### $\inf_{n\in \mathbb{N}^*} \left\{\frac{3^n}{2^n} \right\} > 0$?

I would expect this to be false - the powers of a real number mod 1 should be uniformly distributed on [0, 1] unless there's some reason to expect otherwise. The particular case of the powers of $3/2$...
• 22.8k

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