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Post by Jep Gambardella on Jan 9, 2020 23:09:12 GMT
That is ridiculous. Obviously there are more rectangles than squares. Both numbers are infinite, but one is bigger than the other - just like the number of multiples of 3 is bigger than the numbers of multiples of 5 (even though both are infinite). Actually multiples of 3 can be put into one-to-one correspondence with multiples of 5, and therefore have the same count. This is easy to verify. What's a bit more mind-blowing is that Cantor showed that the points on a line are the same in number as the points in a plane, and therefore their count is the same.
That's only if you accept the premise that all infinite counts are the same.
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