How can two infinite sets not have one to one correspondence with each other?

How can two infinite sets not have one to one correspondence with each other?
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Answer :

You’ve missed what an “infinite set” means. Consider this definition: “Infinite sets are the sets containing an uncountable or infinite number of elements. Infinite sets are also called uncountable sets.” That is, calling a set infinite, simple means it includes an uncountably large number of members. If you list X members, someone could always mention more members. So these are all infinite sets: * All the real numbers between 1 and 2. * All the real numbers between 3 and 4. * All the points on the line x = y. * All the points on the line x = y + 3. There an an infinite number of members of the first set and the second set, and none of the members of the first set are in the second set. Same for the third and fourth sets. Or for “the set of all positive integers” and “the set of all negative integers”.
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