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Oct23-11, 02:47 PM
Firstly, we have many ways of treating infinity as a number: ordinals, extended reals, real projectives, surreals, and the Riemann sphere to name a few. All of these define operations with it, so it is an arithmetic. And by the axiom of choice, there always is a well ordering. Whether we can write that ordering down is a another matter.
So what is the arithmetic of the extended reals?
What is the arithmetic of the Riemann sphere?