This page will list important terms and definitions as we move from unit to unit.
Email me with suggestions on additional terms that you would like to see defined on this page.


additive inverse
– the number, that, when added to another number, gives us zero, which is the identity for addition. For example, the additive inverse of six is negative six, and the additive inverse of negative eight is eight.


identity or identity element – the number that, when combined in a mathematical operation, such as addition or multiplication, gives back an answer that is the original number.

For example, the identity element for addition in the set of real numbers is zero, since zero plus any real number equals that real number.

Similarly, the identity element for multiplication in the set of real numbers is one, since one times any real number equals that number.

integer – All of the counting numbers from one to infinity, zero, and all of the counting negative numbers from negative one to negative infinity.

linear equation – an equation of the form y = (m times x) + b, where m is the slope of the line, b is the number where the graph of the equation crosses the y axis, x is a variable, and y represents some real number.

linear inequality - an equation of one of the following four forms:

y > (m times x) + b
y > or equals to (m times x) + b
y < (m times x) + b, or
y > or equals to (m times x) + b,

where m is the slope of the line, b is the number where the graph of the equation crosses the y axis, x is a variable, and y represents some real number. The

multiplicative inverse – the number that, when multiplied by another number, gives us one, which is the identity for multiplication. For example, the multiplicative inverse of six is 1/6, and the multiplicative inverse of 5/6 is 6/5.

rational number – a fraction, that is, a number that can be put into the form p/q, where both p and q are integers, and q does not equal zero.

real number – the numbers that you will be dealing with in this class; all numbers that are not imaginary numbers (such as the square root of negative one).

reciprocal – another term for multiplicative inverse

“solution of an equation” – we solve an equation for a certain variable – let’s call it “x”. The solution is the number, or number and variable combination that is equivalent to that number.

variable – a symbol that represents something else, such as a number.


variable expression – a mathematical expression that contains at least one variable.