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Post by Jep Gambardella on Dec 23, 2019 4:14:11 GMT
...And... A square is a rectangle, but most rectangles are not squares.George Cantor might disagree with you here. You imply that there are more rectangles than squares. We can map (or make a one-to-one correspondence) between each member of the set of all rectangles and the set of all natural numbers (ie 1, 2, 3...). We can make the same mapping of all squares with the natural numbers. Therefore I would suggest (and I believe Cantor proved) that the set of all rectangles and the set of all squares are the same size. 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).
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