# Useful negation of a statement

#### ver_mathstats

1. The problem statement, all variables and given/known data
Find the useful negation of "X is finite". But you cannot use "not finite".

2. Relevant equations

3. The attempt at a solution
I am very confused as to how to write "X is finite" in a more positive way. I thought I would have just written X is not finite but since we cannot do that I am at a loss.

Thank you.

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#### jim mcnamara

Mentor
What is the antonym "concept" of finite? That which is not finite may also be called _____________ (one word)

#### ver_mathstats

What is the antonym "concept" of finite? That which is not finite may also be called _____________ (one word)
Would it be infinite, since the antonym of finite is infinite?

#### epenguin

Homework Helper
Gold Member
"In-" is just the same thing as "not" so that won't do.

#### pasmith

Homework Helper
"In-" is just the same thing as "not" so that won't do.
"infinite" is not the same sequence of characters as "not finite", and therefore an adequate answer.

#### epenguin

Homework Helper
Gold Member
"infinite" is not the same sequence of characters as "not finite", and therefore an adequate answer.
Would the same thing in another language, say 'pas fini' also be an adequate answer?

I suppose at least you could say that was useful, for some people, which was part of the question.

But I thought the question was really asking for some additional concept.

#### jim mcnamara

Mentor
@ver_mathstats said:
Would it be infinite, since the antonym of finite is infinite?
I believe infinite is what is intended as the answer. So, yes.

However I'm not clear on what @epenguin point is trying to make.

#### epenguin

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Gold Member
"I'm not clear on what @epenguin point is trying to make." jim-mcnamara.

My point that just saying another word is not adding anything of substance, therefore not really useful as the question asked.
You have a word, and you introduce a new word, and you say they mean the same thing.If that is useful, it is a statement only useful about the new word not the thing. Useful to someone who had never heard the second word. Limited usefulness because the formation of the word follows a generally known convention of the language for forming new words, so most people could get there anyway.

I thought, well I know, we all know, what finite means.... er, do we? I mean it is one thing to be able to easily recognise examples, another to say how, what the definition is. Better brush it up. E.g. here - https://en.m.wikipedia.org/wiki/Finite_set . Yes that is what I thought it was, at first, further down it gets complicated. But at least this seems to offer a way. The indication of how to decide whether something is finite or not, that is what I would think can get us to a useful definition.

That could be enough to be going on with.

(Then since we are into very fundamental but yet very theoretical things, I have allowed a certain Wildberger to sow some reservations in my mind about the 'in principle' mentioned in the second sentence of that link. I understand him to say that there "are" finite numbers that not only you couldn't count in practice but in principle you couldn't count in practice, there can be no way to even name them, therefore they, and perhaps the definition, don't mean anything. But I believe his are minority opinions and anyway this is well beyond my normal scientific range and competences so just sayin'.)

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#### PeroK

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Gold Member
2018 Award
I am very confused as to how to write "X is finite" in a more positive way. I thought I would have just written X is not finite but since we cannot do that I am at a loss.

Thank you.
Well, you have to think. How do you know a set is finite? How do you test it?

What if you had a set defined in some way that it was not immediately obvious whether it was finite or infinite? How would you show the set is finite or infinite?

At the very least you should be able to give a definition of what it means to be a finite set.

"Infinite" is not a valid answer. You are asked for some mathematical thinking here.

"Useful negation of a statement"

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