Topic: cardinality list of topics
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10 items are filed under this topic.

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	The cardinality of the prime numbers		2009-11-07
		From Justin: Hello there, I was just wondering since the number of primes is infinite, are they equal to infinity or Aleph-null? Justin Answered by Robert Dawson and Victoria West.
	Cardinality of infinite sets		2009-09-01
		From Brian: I was reading an answer to a question on your site regarding infinite sets (http://mathcentral.uregina.ca/QQ/database/QQ.09.01/carlos1.html), and I think they may have got the answer wrong. I his example, he claims that the set of real numbers BETWEEN 0 AND 1 is larger than the set of positive integers. Please correct me if I am wrong, but I believe those two sets are -- pardon the expression -- equally infinite. For any integer, there is a corresponding real number between 0 and 1, and vice versa. For instance, using the decimal as a "mirror", you can create a mirror image of any real number between 0 and 1 as an integer (i.e. 0.1234 gets mirrored as the integer 4321 -- I could write it out algebraically, if you want, but you get my point) Am I wrong? Thanks, Brian Answered by Victoria West.
	Infinite-Dimensional Spaces		2009-06-26
		From Justin: Hello again, I was also just wondering (in Hilbert Space and Function Space) are there infinite-dimensional spaces larger than each other in terms of cardinality? Thanks a lot for your help again! All the Best, Justin Answered by Victoria West.
	Cantor's cardinality		2009-02-16
		From Justin: Hello, I was just wondering why the infinity from real numbers is smaller than Beth Two in the context of Cantor's cardinality set theory? Justin Answered by Robert Dawson.
	What is larger than infinity?		2003-01-12
		From Dana: What is larger than infinity? Answered by Claude Tardif and Harley Weston.
	Equivalence relations on a set of cardinality n		2002-07-06
		From Siddhartha: what is the no. of equivalence and transitive relations on a set of cardinality n? Answered by Penny Nom.
	Can a infinite set be smaller than another infinite set?		2001-11-29
		From Carlos: Can a infinite set be smaller than another infinite set? If so why? Answered by Chris Fisher and Penny Nom.
	Cardinality of sets		2001-11-19
		From Tania: Show that the cardinality of P(X) (the power set of X) is equal to the cardinality of the set of all functions from X into {0,1}. Show that (the cardinality of the natural numbers set) |N| = |NxNxN|. Show that the cardinality of the set of prime numbers is the same as the cardinality of N+ Answered by Walter Whiteley.
	Subsets of the natural numbers		2001-01-30
		From Christina: How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets? Answered by Penny Nom.
	Infinite sets		2000-04-12
		From Brian Provost: Here's the deal: There are an infinite amount of integers (1,2,3...). Agreed? There are an infinite amount of even integers, too (2,4,6...). Agreed? By convention, infinity equals infinity. Yet common sense tells us there are obviously more integers than there are even integers. Prove this to be true mathematically. Answered by Harley Weston.

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