Riddles and infinities. Riddles and other things that many people don't know are among the things that I love. Here are some of them. 1. Cantor showed us that there are 3 inifinities of diffeent sizes. He called them aleph 0, aleph 1, and aleph 2. Since we can't count in order to see the differences he used a 1-1 match up. As an example If there is a bus where all the people were sitting and all the seats were full we would know that the number of people and seats are equal. The aleph 0 set contains the natural numbers (1, 2, 3.....). If we compare them to only the even numbers (2, 4, 6....) we see that every natural number has an even number that matches up (simply multiply by 2) and vice versa. these 2 infinities are equal in size. Any other set that we can list that will contain them all (fractions (1/1, 1/2, 2/2, 2/1 ......) for example) are also aleph 0, because we can match them up with 1, 2, 3.... simply by numbering the list. ...
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