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Re: Non-Euclidean Arithmetic
Posted:
Sep 16, 2012 2:44 PM
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On Sat, Sep 15, 2012 at 1:37 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
> Paul Tanner III Says:
>>>Repeated addition is merely a derivable property of the two operations of such a field like the real numbers, derived in such a field from just some of the algebraic properties
>
> Joe N said:
>>Says you. I say it refers to a family of related procedures for computing addition and as such is a proud and rather ancient member of the incredibly important part of mathematics known today as computational mathematics.
>
> In addition, it can also refer to various *definitions* of addition; to take an example, as in Peano Arithmetic.
>
Only in the natural numbers and with some work, the integers. In the rational numbers a new definitions for multiplication has to be given in terms of the newly defined numbers called rational numbers, defined as equivalence classes of ordered pairs of integers.
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