# BASIC ALGEBRA GLOSSARY

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Title Description
i, Square Root of -1 The small-case i is reserved for the square-root of a negative one; the square of i is -1.
Identity As opposed to a conditional statement that is sometimes true, an Identity will always be true.
The multiplicative identity is 1; the additive identity is zero.
Identity Property of Addition The Identity Property of Addition says that adding zero to (or subtracting zero from) any real value will not change the value.
Identity Property of Multiplication The Identity Property of Multiplication says that multiplication of a real value by one (or division by one) will not change the value.
If-and-Only-If (Iff) A statement that shows a condition both necessary and sufficient for the assertion.
If-Then Statement The classic biconditional statement is often phrased as an If-Then proposition.
Impossibility Despite what some "possibility thinkers" espouse, some things are mathematically impossible.
For example, an exact real number cannot be simultaneously irrational and rational.
Incircle A circle inscribed within a regular polygon (or any triangle) is an Incircle.
In a regular polygon, the radius of the Incircle is the apothem.
Inconsistent Inconsistent equations have no simultaneous solution.
Increasing If the values in the range of a function increase as the values of the domain increase, the function is said to be Increasing.
Independent Variable The set of values from the domain of a function comprise the values for the Independent Variable, the input variable into the function.
Inductive Logic Inductive Logic is the logic of after-the-fact, or a posteriori.
It results from observation of transpired events.
Inequality Generally of one of the following four forms: less than, less-than-or-equal-to, greater than, or greater-than-or-equal-to.
Infinite In common language, not countable in any practical manner.
In math, having no bounds or boundary.
Infinite Geometric Progression When a geometric progression has a common ratio less than one (technically, a common ratio whose absolute value is less than one), then the Infinite Geometric Progression will converge to a limit.
Infinitesimal Infinitely small is Infinitesimal, so tiny that it occupies no space.
While in human terms anything really small (a molecule) is Infinitesimal, in math the term means approaching zero in size.
Infinity That without bound; limitless.
Inscribed Circle This term is the same as Incircle, a circle inscribed within a polygon.
Integer An Integer is a whole number or its negative.
When expressed as a decimal, an Integer has nothing to the right of the decimal point (in American style).
Interest Given the time-value-of-money, Interest is generated on a sum of capital as time passes.
Interior Interior means within or "in-between."
Interquartile Range The Interquartile Range is the half of overall data between the 25th and 75th percentiles.
Intersection Where geometric entities cross, or where sets have common elements, is termed an Intersection.
Interval The space or region between two defined values is an Interval.
Interval Notation With brackets or parentheses, depending on whether endpoints are included in the set, Interval Notation expresses the solution set for an inequality.
Invariant Constant.
Not changing.
Static.
That which does not vary.
Inverse Inverse carries a lot of meanings within the language of mathematics.
Inverse Variation Variables or factors that multiply to a constant value are said to be in a relation of Inverse Variation.
Inverse, Conditional Given an initial if-then statement, the negative of both the hypothesis and conclusion provides the Inverse to the original statement.
Inversely Proportional When the product of two variables is a constant the variables are said to be Inversely Proportional to one another.
Iota The ninth letter of the Greek alphabet, Iota means a very small amount.
Irrational Number An Irrational Number cannot be expressed exactly as the ratio of two integers.
Irrational Numbers, when expressed as decimals, never repeat or terminate.
Iteration A procedure that repeats, typically by adding some value to a variable in the process with each new calculation is called an iterative process, and each cycle of the calculation is an Iteration.
A computational procedure in which a cycle of operations is repeated, often to approximate the solution to a problem.

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