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Question:
I have a question about what was said in the first response on note 400. How can you say that the {infinite set of all real numbers} is greater than the {infinite set of all integers}? Please go into a lot of depth for I thought I was clear on this concept. Thank You



Replies:
This can't be answered in a lot of depth in only one screenful of text. But try looking up 'Cantor's diagonal argument'. The idea is that if there are as many real numbers as integers, you should be able to make a table listing in one column all integers and in the other all reals. Contor's argument shows that whenever you think you've made such a list, you can construct a real number that isn't on the list. Thus the set of real numbers is greater than the set of integers.

jan p anderson


A good source is *Advanced Calculus* by Angus E. Taylor, p 479-80.

billrob



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