UMBC CMSC203, Discrete Structures, Spring 2009

⇐ Rules of Inference Direct Proofs ⇒

Proofs are written in English

Do not worry overly much about the names of these rules of inference. For this class, if you use the inferences correctly, that is good enough. You don't have to remember which one is modus ponens and which one is modus tollens. In fact, if you flip through almost any math book, you will not find any mention of "modus ponens" or "disjunctive syllogism" in the proofs (with the possible exception of books on logic). This is because applying a rule of inference is such a small step in the reasoning process that it would not be helpful to the reader to point out that you have just used a particular rule.

Mathematical proofs are usually written in paragraph form and complete sentences. Even a sentence that uses mathematical notation should be a complete sentence when read aloud. For example:

If the vertex xA, then we color x red.
This sentence should be read aloud as "If the vertex x is an element of A, then we color x red." The verb in the "if" clause is the ∈ symbol.

Most of the rules for writing you learned in English classes are applicable in mathematical writing. For example, when you start a new topic, you should start a new paragraph. You should also avoid run-on sentences, they are hard to decipher. About the only exception is the advice that you vary the vocabulary. You might have been told in a writing class to use different words to describe an object so you do not repeatedly use the same word. In mathematical writing, you should actually stick to the same terminology. For example, although the terms "vertex" and "node" are used interchangeably, you should stick to one or the other and not use both words in the same writing. Thus, in mathematical writing, you do not need to wrack your brains to think up "exciting" adjectives and adverbs. For example, a vertex without any edges is called an "isolated" vertex. You will always call this an isolated vertex. You won't ever have to describe the vertex as "lonely", "alienated", "dejected" or "outcast".

Instead, concentrate on the 4 C's of mathematical writing: try to be clear, concise, convincing and correct.

⇐ Rules of Inference Direct Proofs ⇒

Last Modified: 17 Sep 2013 22:24:26 EDT by Richard Chang
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