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Unformatted text preview: Math 100 Variables and Quantifiers Martin H. Weissman It is difficult to discuss interesting mathematics without using variables. Without variables, one can make statements about specific numbers and arithmetic for example, but one can not state a general theorem. On this day, we look at variables in the language of algebra. 1. Usage of variables in English Remember that variables are analagous to pronouns. However, one problem with mathematical language is that a variable is usually just a letter, like x or θ , whereas pronouns (in English and most other languages) have much more variety expressing various meanings, such as “he”, ”it”, ”someone”, ”everyone”, ”this”... etc. Since variables carry less meaning than pronouns, one must always clarify the usage of a variable with helping phrases. 1.1. Using a letter to directly stand for a known quantity. Sometimes, a letter is used simply as an abbreviation for a quantity. Consider the following (classic) sentence: There are five times as many students in the math department as professors. If you wish to express this relationship using algebraic language, using letters S and P , for example, you absolutely must describe what the letters stand for. The following is a good template to use: Let S be the number of students in the math department. Let P be the number of professors in the math department. If you write a sentence like “ S = Students”, you will be penalized!! Other examples of using a variable in this way are the following: • Let N be the number of prime numbers between 1 and 1000000....
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- Fall '08
- Math, Natural number, Prime number