Choice and Infinitesimals
We prove here Theorem 7.10 which offers three equivalent forms of the Axiom of Choice. We then use AC to construct a system of numbers called the Hyperreal numbers (ℍℝ). This system extends ℝ as ℝ extended ℚ and ℚ extended ℤ. ℍℝ contains both infinite numbers and infinitesimals.
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