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.

Clarification 
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.
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.

