Common Mistakes and Good Practice
Definitions of Supplementary Statements
Conjectures are built on other conjectures. They can be subdivided into the following parts:
- Theorem
- A very important true statement.
- Proposition
- A less important by still interesting statement.
- Lemma
- A true statement used to prove other statements.
- Corollary
- A simple consequence of a theorem or a proposition.
Finishing Proofs
At some point in a proof, you’ll have established all the essential facts you need. Resist the temptation to quit and leave the reader to draw the “obvious” conclusion. Instead, tie everything together yourself and explain why the original claim follows.
In addition, at the end of a proof use the Latin phrase, “$_\text{QED}$” or $\square$ to show that you have finished the proof.