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2 articles trouvés pour ce sujet.
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Cardinality of infinite sets |
2009-09-01 |
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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. |
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Infinite sets |
2000-04-12 |
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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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