Ones and twos. Describe a one-to-one correspondence between the set of all decimal numbers between 0 and 1 that are made with only 1’s and 2’s (like 0.1211212212212... ) and the set of all decimal numbers between 0 and 1 that are made with only 3’s, 4’s, 5’s, and 6’s (like 0.36543546354554. . . ). (Hint: Decimals made of 1 ‘sand 2’s only can have their first two places 0.11. .. 0.21... , 0.22....)
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