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10 articles trouvés pour ce sujet.
The cardinality of the prime numbers 2009-11-07
Justin pose la question :
Hello there, I was just wondering since the number of primes is infinite, are they equal to infinity or Aleph-null? Justin
Robert Dawson and Victoria West lui répond.
Cardinality of infinite sets 2009-09-01
Brian pose la question :
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

Victoria West lui répond.
Infinite-Dimensional Spaces 2009-06-26
Justin pose la question :
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
Victoria West lui répond.
Cantor's cardinality 2009-02-16
Justin pose la question :
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?


Robert Dawson lui répond.
What is larger than infinity? 2003-01-12
Dana pose la question :
What is larger than infinity?
Claude Tardif and Harley Weston lui répond.
Equivalence relations on a set of cardinality n 2002-07-06
Siddhartha pose la question :
what is the no. of equivalence and transitive relations on a set of cardinality n?
Penny Nom lui répond.
Can a infinite set be smaller than another infinite set? 2001-11-29
Carlos pose la question :
Can a infinite set be smaller than another infinite set? If so why?
Chris Fisher and Penny Nom lui répond.
Cardinality of sets 2001-11-19
Tania pose la question :
  1. 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}.

  2. Show that (the cardinality of the natural numbers set) |N| = |NxNxN|.

  3. Show that the cardinality of the set of prime numbers is the same as the cardinality of N+

Walter Whiteley lui répond.
Subsets of the natural numbers 2001-01-30
Christina pose la question :
How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets?
Penny Nom lui répond.
Infinite sets 2000-04-12
Brian Provost pose la question :
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.
Harley Weston lui répond.



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