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

General Suggestions
The first step, whether we are trying to prove a result or we are trying to
understand someone else's proof, consists of clearly understanding what are
the assumptions (hypotheses) made in the statement of the theorem and
what is the conclusion to be reached. In this way, we are estabhshing the
starting and ending points of the logical process that will take us from
the hypotheses to the conclusion. We must understand the meaning of the
hypotheses so we can use the full strength of the information we are given,
either implicitly or expUcitly, to achieve the desired result. It is essential to
check all technical words appearing in the statement and to review the
definitions of the ones for which the meanings are not clear and famiUar.
EXAMPLES
1. Suppose we are going to prove the following statement:
// a triangle is equilateral, then its internal angles are equal.
We start with the following information:
i. the object is a triangle (explicit information); and
ii. the three sides have the same length (explicit information from the
word equilateral).