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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Sign up to join this communityI understand there is a symbol for infinite. Is there one for finite?
I searched and found there is none. How is finite represented symbolically?
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.
How about using $$\not\infty$$
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".
Writing instead of symbolizing is a very bad idea but some rare cases. The reasons are:
For this I think is a good idea use the symbol, as noted before, $\not\infty$.
This is too long for a comment so I write an answer.
EDIT:
A more convincing, and objective argument for my apology: nobody write number or basic operands with words... we don't write $\text{"two more two"}$ when we are doing mathematics... we write $"2 + 2"$.
When we are using words in advanced mathematics this is because doesn't exist a good symbolic way to express complex things (by now), but this doesn't mean that is the "best" or "correct" way to do.
Just compare words, mathematical notation of the roman empire before the use of Indian numbers, with the actual notation. The evolution tends to destroy words in favor of the extremely more efficient pure symbol... but what is needed is a good symbology, if this doesn't exist of course the best is just write words and describe things with natural language.