David Richeson: Division by Zero

I prepared the following handout for my Discrete Mathematics class (here’s a pdf version).

**Definition** — a precise and unambiguous description of the meaning of a mathematical term. It characterizes the meaning of a word by giving all the properties and only those properties that must be true.

**Theorem** — a mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results.

**Lemma** — a minor result whose sole purpose is to help in proving a theorem. It is a stepping stone on the path to proving a theorem. Very occasionally lemmas can take on a life of their own (Zorn’s lemma, Urysohn’s lemma, Burnside’s lemma, Sperner’s lemma).

**Corollary** — a result in which the (usually short) proof relies heavily on a given theorem (we often say that “this is a corollary of Theorem A”).

**Proposition** — a proved…

View original post 171 more words