Find the mistakes in the “proofs” shown.
Exercise
Theorem: The sum of any two even integers equals 4k for some integer k.
“Proof: Suppose m and n are any two even integers. By definition of even, m = 2k for some integer k and n = 2k for some integer k. By substitution,
m + n = 2k + 2k = 4k.
This is what was to be shown.”
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