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**Prove 2 ∤ 1 , assuming the existence of the natural numbers and integers along with their most basic arithmetical and ordering properties. (Not allowed to use rational numbers)**

**2. Let and b be integers. We say a divides b if there exists an integer k such that ka = b.**

**3. Well, my intuition says to start by saying that if a | b then there exiests an integer k such that 2*k = 1. Obviously such integer doesn't exist. I was thinking about using prop 6 (which I've already managed to prove on my on) from http://primes.utm.edu/glossary/xpage/divides.html to say If 2 divides 1 then 2 divides 1c for any integer c. Meaning 2 divides every integer, which it does not. I don't know if that's enough. Would appreciate some input**