Martin Sleziak's room

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9:24 AM

I'm not sure whether to put this doubt into a question on the main site, or whether there's a chatroom for it... My doubt is «Is there a sequence in R, for which either limsup or liminf are not defined?»

4 hours later…

Martin Sleziak

1:07 PM

@Anoldmaninthesea. I think that the Calculus and analysis room would be fine.

In any case, as far as I can tell there is no such sequence. (Assuming you allow values to be $\pm\infty$.)

One of several equivalent definitions of limit superior is $\limsup x_n = \lim_{n\to\infty} \sup_{k\ge n} x_k$.

We know that limit of a monotone sequence of (extended) real numbers exists (if we allow infinite values).

The sequence $\sup_{k\ge n} x_k$ is monotone.

An old man in the sea.

1:43 PM

Many thanks Martin ;)

2 hours later…

Ninja hatori

4:01 PM

Q: about isometry classes

This is Theorem 2.3.8 from Scharlau's book Quadratic and Hermitian Forms I know that $\mathbb{F}_q$/$\mathbb{F}_q^2$ has index 2 so it has only two elements ; since 1 is also square in $\mathbb{F}_q$ why it is one of element of $\mathbb{F}_q$/$\mathbb{F}_q^2$. Also what is meaning form $\langl...