Question: Please explain step by step, thanks! This question is designed to go carefully through the proof of the Archimedean Property of the natural numbers, which

Please explain step by step, thanks!

This question is designed to go carefully through the proof of the Archimedean Property of the natural numbers, which we have discussed in the lecture notes. Theorem (the Archimedean Property): The set of natural numbers N is not bounded above. Proof: 1. Assume for a contradiction that N is bounded above. 2. Then, since N is non-empty, N has a least upper bound, call it b. 3. If m E N, then m + 1 E N also, hence m + 1 5 b. 4. Thus, m b for all m E N O E. if I is any other upper bound then b 5 1 O F. if I is any other upper bound then N

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