General Structure of a Theorem
The purpose of a theorem is to present a mathematical truth. Of course, just stating that something is
true does not make it so. Mathematics history is littered with “theorems” that later were discovered to be
false. What that means is the original proof was faulty. Our goal is to develop proofs that are solid. This
sheet attempts to show how to minimize the chance of error. A theorem has two parts: its statement and
its proof.
The Theorem Statement
is subdivided into two constituents:
Hypotheses
(these are statements that are assumed to be true without question; there is no option
for believing them or not)
Conclusions
(these are statements of what is to be proven)
It is important to be able to identify the hypotheses and conclusions in a theorem statement.
The proof
is a series of statements leading the reader to incontrovertible agreement that the conclusions
are true under the assumption that the hypotheses are true. There are various types of statements in the
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Brigham
 Mathematical proof

Click to edit the document details