Prove that every Non-Empty set of Positive Integers contains a "Least Element".
(In reply to
Proof by Contradiction by friedlinguini)
I came up with something similar:
Let S be a non-empty set of positive integers. Let I be a binary sequence indexing the integers in S, where bit i of I is 1 if and only if i is in S. For example, if S is {1, 3, 5}, then I is 10101000...
Since S is non-empty, I clearly has a first occurrence of 1 somewhere. That occurrence of 1 clearly corresponds to the least element of S.
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Posted by Caleb
on 2019-04-02 23:23:02 |
re: Proof by Contradiction
