Why Study Math? – Functions and Rules

One of the most important concepts in mathematics is that of a function. Although the topic of function can appear abstract, it is nothing more than a specific rule between two sets of mathematical objects. These sets are usually numbers, but they do not have to be restricted to such mundane entities. The sets might consist of more interesting objects, such as matrices or vectors. This notwithstanding, a function is nothing more than a rule that associates with each member of one set another member of the other set. Here we discuss this exciting concept in a little more detail so that the next time you see or hear about it, rather than avert your eyes or go cowering away in fear, you jump right in on the conversation.

Before we introduce the concept of function let us define what we mean by a set. A set is simply a well-defined collection of objects. Sets can be defined by listing their specific elements as in
S = {1, 2, 3} or by definition such as S = {2n| n is an integer} to define the infinite set of even integers. A function is simply a rule between two sets, such that this rule assigns to each element of the first set, call it set A, a unique element of the second set, call it set B. For example, let set A = {1, 2, 3} and B = {2, 4, 6}. We traditionally let the letter f stand for a function. We can define a function f from set A to B such that we associate 1 in A with 2 in B; 2 in A with 4 in B; and 3 in A with 6 in B.


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