Table of Contents
An Introduction to the Theory of Groups
A group is a set of elements together with a binary operation (usually denoted by *) that satisfies four properties:
Closure: For all a, b in the group, a * b is also in the group.
Associativity: For all a, b, c in the group, (a * b) * c = a * (b * c).
Identity: There exists an element e in the group such that a * e = a for all a in the group.
Inverses: For every a in the group there exists an element b such that a * b = e, where e is the identity element.
Fact About Linear Inequalities
A linear inequality is an equation involving two variables that is linear in one of the variables. Linear inequalities always have a graph that is a line. The line will be solid if the inequality is true for all values of the variable on the line, and it will be dashed if the inequality is not true for some values of the variable on the line.
