(Mathematical) Definitions

In this video, we discuss the mathematical meaning of a definition. As examples, we learn the definition of parity and divisibility.

This is lecture 1 (part 1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 3120 - Transition to Advanced Mathematics at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:

[arghyadas]

Hi, Can You Please Suggest Me A Textbook That I Can Use To Follow This Lecture Series?

[zihaowang]

Hi, thank you for this video! I had a question about the use of symbols like n in the definition of the even number. The definition states "we say an integer n is even, if n = 2a for some integer a", I guess what I am confused about is when n is added to the mix, what is the effect of n here? Is it just placed after "an integer" to refer back to the integer that we considered, i.e. so we don't have to say "that integer" later on, (e.g. instead of saying "we say an integer is even if that integer is 2a for some other integer a"), or is it doing something more? Similar question on the use of the symbol a, is it just to refer to the "some integer", so we don't have to say "n is 2 times some integer" instead?