# Symbol for finite

I understand there is a symbol for infinite. Is there one for finite?

I searched and found there is none. How is finite represented symbolically?

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In writing, you'll probably be better off being clear and using words, not symbols. –  lhf Jun 18 '12 at 12:57
Possible duplicate of this question? –  Zev Chonoles Jun 18 '12 at 13:16
@lhf: do you mean to say that symbols will be more handy than words when talking? –  tomasz Dec 8 '12 at 1:18

I have never seen a notation for 'finite,' but what I do very often see is denoting something finite as simply being less than infinity. For example, $|A| < \infty$, or $[G:H] < \infty$.

Small thing I'd like to add: Of course something like $[G:H] < \infty$ isn't technically meaningful, but it certainly gets the point across and in my experience at least seems to be pretty standard.

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What's not technically meaningful about it? It's a comparison between two cardinalities. –  Qiaochu Yuan Jun 18 '12 at 14:21
@QiaochuYuan: True, it does work in that case if we let $\infty$ represent some transfinite cardinal number. I should have used the second example there, and in fact I will edit it. (and sorry for the late reply) –  Alex Petzke Jun 20 '12 at 15:14
I don't see what's not technically meaningful about $[G : H] < \infty$ either. You are committing a fairly small abuse of notation in identifying a finite cardinal with a natural number. One can make perfect sense of the poset $\{ 1, 2, ... \infty \}$. –  Qiaochu Yuan Jun 20 '12 at 15:45

I'm guessing you mean the symbol $\infty$, for a non-specific non-finite cardinality. In this case, in the same way you would say $|X|=\infty$ to mean "the set $X$ has infinitely many elements", I would write $|X|<\infty$ to mean "the set $X$ has finitely many elements".

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He doesn't say he is working with cardinals. When we have a function $f$ with (according to its definition) values in the extended real numbers $[-\infty,+\infty]$, and we want to emphasize that a certain value $f(x)$ is finite, we may write $|f(x)| < \infty$. When we have a series $\sum a_n$ and we want to say it converges absolutely, we may write $\sum |a_n|<\infty$. –  GEdgar Jun 18 '12 at 13:45
Sure, I used cardinals as an example. (This is why I like Alex's answer better, because he gives two examples). –  Matt Pressland Jun 18 '12 at 13:48

How about using $$\not\infty$$

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I had the same idea, but didn't know \not. –  draks ... Jun 19 '12 at 10:23
You might want to consider using "\!" a few times to write $\not\!\!\infty$. Just typographical concerns ;) –  Alex Nelson Jun 20 '12 at 15:48
It just doesn't look any good ): –  Elements in Space Jan 5 '13 at 17:19