epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

Collection of Proofs
The following collection includes "proofs" that are correctly prepared and
those with flaws in them, proofs that can be found in the mathematical
tradition and those prepared by students. Examine the "proofs" presented
here, judge their soundness, improve on them; in short, pretend you are the
teacher and grade the material presented.
THEOREM 1.
The number 1 is the largest integer.
Alleged Proof. Suppose the conclusion is false. Then let n > 1 be the
largest integer. Multiplying both sides of this inequality by n, yields n^ > n.
This is a contradiction, because n^ is another integer larger than n. Thus, the
theorem is proved. •
THEOREM 2. The value of the expression y sysTv^^S is 3.
Alleged Proof.
Let
N sysyaVWJT^ 115