Date: Tue 11/10/98 10:08 AM
From: Alex Bogomolny
Dear Toby:
I do not know what to tell with regard to your assertion that "you believe you know the number 1, because 0 plus 1 equals 1." It simply does not make sense to me. One can't define something (1, in your case) in terms of that something. Look into Peano's axioms:
../do_you_know/mul_num.shtml#peano
In order to define what interger numbers are you have to start somewhere, say at 0 or 1 (but just one of them) and assume some basic property of those numbers. Peano's axioms assume that you accept the notion of "successor." - which is equivalent to adding 1. The fact is that once you know how to add 1, you also know how to add all other numbers.
In this sense, addition is equivalent to passing to a successor. Perhaps the latter is a more simple operation (Peano thought so.) Otherwise, addition is an operation which inherent to the natural numbers and counting. "Plus" is just a notation for this operation.
All the best,
Alexander Bogomolny
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