Find the mistakes in the “proofs” shown.
Exercise
Theorem: The difference between any odd integer and any even integer is odd.
“Proof: Suppose n is any odd integer, and m is any even integer. By definition of odd, n = 2k + 1 where k is an integer, and by definition of even, m = 2k where k is an integer. Then
n − m = (2k + 1) − 2k = 1.
But 1 is odd. Therefore, the difference between any odd integer and any even integer is odd.”
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