infinity is not a number
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basically manipulations that hold for any nonzero number a,b,c.. like a/b = c/b --> a=c
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Problem: Some axioms are true for things that are not numbers. "Things equal to the same thing are equal to each other."
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"I am me" - Reflexive Axiom If A is C, then A or B is C or B - Additive Axiom If A is B then A and C is B and C - Multiplicative Axiom This stuff true for anything, not just numbers.
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Then it depends on what infinity you're talking about. Cardinal arithmetic encapsulates pretty well arithmetic with cardinal numbers corresponding to the cardinality of the natural and the real numbers, which are infinite, and likewise for ordinal arithmetic.
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