Beginning today, and throughout the rest of your college mathematical career, you are going to be continually presented with definitions, theorems, lemmas, corollaries, axioms, and a multitude of other mathematical knick-knacks. Each has its place in the mathematical collage and the more familiar you are with these distinctions, the better you will fair in this, and future, mathematics courses.

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Definitions in mathematics are similar to definitions elsewhere in that they are statements we accept because we must agree to some common language in order to communicate effectively with each other. On the other hand, mathematical definitions differ from traditional definitions in that multiple meanings for the same defining word or phrase are incredibly rare.

In the “real world,” we have the luxury of being able to ask what the definition of something is a few times and, in general, people forgive our ignorance. For example, most people would forgive you if you had to ask repeatedly for the definition of the Higgs Boson (a.k.a. the Higgs particle). It’s a tough definition to grasp.

When taking a mathematics course, it is incredibly important that you familiarize yourself with the definitions as soon as they are presented. The rest of the material is generally built upon a strong knowledge of these definitions. To help you get used to mathematical definitions, I will constantly use the terms that we define. Moreover, I will make every effort to be consistent with my language.

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*is something that we state concerning the meaning of a word or phrase. In general, when someone defines something (by giving it a name or a “naming phrase”) there is little else you can say to refute that definition. For example, a “cell phone” is called a cell phone because someone else did not call it a “tark phone” first. Unfortunately, some definitions are ambiguous.***definition**Definitions in mathematics are similar to definitions elsewhere in that they are statements we accept because we must agree to some common language in order to communicate effectively with each other. On the other hand, mathematical definitions differ from traditional definitions in that multiple meanings for the same defining word or phrase are incredibly rare.

In the “real world,” we have the luxury of being able to ask what the definition of something is a few times and, in general, people forgive our ignorance. For example, most people would forgive you if you had to ask repeatedly for the definition of the Higgs Boson (a.k.a. the Higgs particle). It’s a tough definition to grasp.

When taking a mathematics course, it is incredibly important that you familiarize yourself with the definitions as soon as they are presented. The rest of the material is generally built upon a strong knowledge of these definitions. To help you get used to mathematical definitions, I will constantly use the terms that we define. Moreover, I will make every effort to be consistent with my language.