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Hi everybody,

How is the number system created and defined? I am talking about the natural numbers, but I am not actually asking about the definition and properties of N (Peano) but for the way that we have agreed to produce numbers. I mean, we have defined ten digits:0,1,2,3,4,5,6,7,8,9 and all the natural numbers can be written as a series of these digits. I would like to know if there's any logic behind these ways we have for writing numbers.

For example, we have decided that the successor of 9 is 10, of 19 is 20, of 99 is 100 etc. Why we have chosen this way to create any number, as big as we want? A number with k digits n(1),n(2),...,n(k) ,beginning from left to right with n(k) and ending with n(1) is actually defined like this:

=n(k)*(10^(k-1))+n(k-1)*(10^(k-2))+...+n(2)*10+n(1) ? (I am referring to the decimal system) Is this just a convenient way that also is in agreement with the axioms and properties of naturals?

I hope you understood what I am asking (i know it's not very clearly stated )

Thanks

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# Construction of number system

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