ADVANCED ALGEBRA GLOSSARY
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Title  Description  

i, Square Root of 1  The smallcase i is reserved for the squareroot 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 Matrix  The Identity Matrix is a square matrix with zeros everywhere except on the main diagonal, which has all elements equal to one. It is the product of a matrix and its inverse. 

IfandOnlyIf (Iff)  A statement that shows a condition both necessary and sufficient for the assertion. 

IfThen Statement  The classic biconditional statement is often phrased as an IfThen proposition. 

Imaginary Number  Imaginary Numbers exist, but we do not call them "real."  
Implicit  Implied as opposed to absolutely expressed, Implicit functions typically have two (or more) variables on one side of the equation. 

Impossibility  Despite what some "possibility thinkers" espouse, some things are mathematically impossible. For example, an exact real number cannot be simultaneously irrational and rational. 

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. 

Indeterminate  Often a resultant fraction like 0/0 is an Indeterminate form that requires more analysis to determine its true nature, depending on the functions involved. 

Inductive Logic  Inductive Logic is the logic of afterthefact, or a posteriori. It results from observation of transpired events. 

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. 

Infinite Series  Any series of terms whose progression has an unlimited (limitless) number of terms is an Infinite Series. 

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. 

Inflection  On the graph of a function, a point of Inflection is where the curve begins to "bend the other way."  
Inner Product  With vectors, the dot product is considered an Inner Product. 

Inscribed Circle  This term is the same as Incircle, a circle inscribed within a polygon. 

Instantaneous Velocity  The reading at any instant on a speedometer gives an Instantaneous Velocity. To be precise, the speedometer gives an instant snapshot of speed (only) with no direction; physical velocity has both magnitude and direction, as a vector. 

Interest  Given the timevalueofmoney, Interest is generated on a sum of capital as time passes. 

Intermediate Value Theorem  The IVT basically says that between two different values is an intermediate value somewhere between the extremes. 

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 Cosecant  Given a number, this function returns the angle whose cosecant is the given number. 

Inverse Cosine  Given a number, this function returns the angle whose cosine is the given number. 

Inverse Cotangent  Given a number, this function returns the angle whose cotangent is the given number. 

Inverse Function  For most functions in Cartesian coordinates, the inverse function is the mirror image around the x=y line. 

Inverse Secant  Given a number, this function returns the angle whose secant is the given number. 

Inverse Sine  Given a number, this function returns the angle whose sine is the given number. 

Inverse Tangent  Given a number, this function returns the angle whose tangent is the given number. 

Inverse Trigonometric Function  Given a number, this function returns the angle whose trig function is the given number. 

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 ifthen statement, the negative of both the hypothesis and conclusion provides the Inverse to the original statement. 

Inverse, Matrix  When two matrices multiply to produce the identity matrix, each is said to be the Inverse Matrix of the other. 

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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