# Talk:Infinite set

WikiProject Mathematics (Rated Start-class, Mid-priority)
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Mathematics rating:
 Start Class
 Mid Priority
Field: Foundations, logic, and set theory

## Definition

I am curious why "a set with infinitely many elements" was considered a non-definition. --Fell Collar 16:51, 9 April 2006 (UTC)

Because it is circular, i.e. you are defining "infinite" in terms of "infinite". An infinite number is simply the cardinality of an infinte set. We MUST define it for sets first, not for numbers first, because numbers are a derivative concept relative to sets. If you go to the article on finite sets, you will see that it contains real definitions of finite for sets. JRSpriggs 04:36, 10 April 2006 (UTC)
Okay, that makes sense. Thanks very much. --Fell Collar 20:01, 11 April 2006 (UTC)

## For the layman

Maybe someone should put in the explanation of why real numbers is an uncountable set at the beginning. I guess there is a page specifically about uncountable infinities, but maybe save the touble by explaining your example real quick. Its because there are infinite elements of the set between 1 and 2 so, while you know 2 is an element, you could never count to it, right? I would just add it, but I don't know if its necessary and I don't know if my minor in logic is enough qualification to confidently contribute to the article. Dayleyj 21:50, 23 October 2007 (UTC)

Any correct explanation of why the real numbers are uncountable must be too lengthy to put into this article. It is explained elsewhere. I added another link to "uncountable set" to help people find it. See Cantor's diagonal argument. JRSpriggs 01:15, 25 October 2007 (UTC)
Thanks, that was really what I was looking for. Dayleyj 00:15, 28 October 2007 (UTC)

## infinite set?

Does the set of all fractions qualify as an infinite set? --Neptunerover (talk) 17:07, 25 January 2010 (UTC)

For questions that are not related to improving the article I suggest using WP:Reference desk/Mathematics. You are likely to get better responses there. Hans Adler 17:22, 25 January 2010 (UTC)
Thank you. I was just thinking that if they do qualify, then perhaps the article could mention that, unless such is far too basic of a notion to require mentioning. --Neptunerover (talk) 05:00, 26 January 2010 (UTC)
Although I suppose there must be a limit when providing examples. One cannot expect them all to be covered. --Neptunerover (talk) 05:06, 26 January 2010 (UTC)

## Failure

The article fails to mention the fact that Galileo noted that phrases such as "as many as" are not applicable to infinite sets. In effect, Galileo was denying the existence of infinite sets. — Preceding unsigned comment added by 88.150.234.8 (talk) 08:39, 3 July 2014 (UTC)

See Two New Sciences#Infinity. — Preceding unsigned comment added by 88.150.234.8 (talk) 08:46, 3 July 2014 (UTC)
See Galileo's paradox. Salviati represents Galileo. — Preceding unsigned comment added by 88.150.234.8 (talk) 08:52, 3 July 2014 (UTC)