. The whole literate world has been taught that every nonnegative integer can be represented by a finite string of digits, and that different strings of digits correspond to different integers. None of this is in our axioms, so it must be established. You know that the string 365 means 5+6 ∙ 10+3 ∙ 100 and you know that the string 371 means 1+7 ∙ 10+3 ∙ 100. These sums add up to different integers. Are you sure? How do you know? Are you equally sure when you have two strings of 400 digits that are not exactly the same? And while we are questioning basic things, here is another problem: In elementary school you learned how to add strings of integers like 365 and 371. How did you do it? And why does it work? Can you write down the instructions so that someone could add other numbers? How did your elementary-school teacher explain addition to you?
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