A statement that is always true. The equations 5 = 5, 7 + 4 = 7 + 4, and x + 8 = x + 8 are examples of identities.
Identity property for addition
For any real number a, a + 0 = a = 0 + a.
Identity property for multiplication
For any real number a, a(1) = a = 1(a).
i, defined as .
A fraction in which the numerator is greater than or equal to the denominator. The fractions are all improper fractions.
The smallest unit of length in the American system. 12 inches = 1 foot.
An equation that has no solution.
Inconsistent system of equations
A system of equations that does not have a solution.
Inconsistent system of linear equations
A system of linear equations that has no solution.
Two equations that are not dependent are said to be independent.
Index of a radical
Indicates what type of a root is being taken. The index of a cube root is 3. In , the 3 is the index of the radical. In , the index is 4. The index of a square root is 2, but the index is not written in the square root symbol, as shown:
A mathematical statement expressing an order relationship. The following are inequalities:
The symbol that is used to indicate whether a number is greater than another number or less than another number. Since 5 is greater than 3, we would write this with a "greater than" symbol as follows 5 > 3 The statement "7 is less than 12" would be written as follows: 7 < 12.
A set that has no end to the number of elements that are within it. An infinite set is often indicated by placing an ellipsis (...) after listing some of the elements of the set.
The numbers in the infinite set.
Intercepts of an equation
The point or points where the graph of the equation crosses the x-axis or the y-axis or both. (See x-intercept.)
The money that is paid for the use of money. If you deposit money in a bank, the bank uses that money and pays you interest. If you borrow money, you pay the bank interest for the use of that money. Simple interest is determined by the formula I = P x R x T. Compound interest is usually determined by a table, a calculator, or a computer.
Intersection of sets
The intersection of set A and set B, A B, is the set of elements that belongs to both set A and setB.
If (x) is a one-to-one function with ordered pairs of the form, (x , y), its inverse function, (x), will be a one-to-one function with ordered pairs of the form (y, x).
Inverse function of a one-to-one function
That function obtained by interchanging the first and second coordinates in each ordered pair of the function. .
Inverse property of addition
For any real number a, a + (-a) = 0 = (-a) + a.
Inverse property of multiplication
For any real number .
When a variable y varies inversely with x, written , where k is the constant of variation.
Invert a fraction
To invert a fraction is to interchange the numerator and the denominator. If we invert , we obtain the fraction . To invert a fraction is sometimes referred to as to take the reciprocal of a fraction.
Numbers whose decimal forms are nonterminating and nonrepeating. The numbers ...are irrational numbers.
A fraction that cannot be reduced (simplified) is called irreducible.
A triangle with two sides equal.
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