 # Glossary Entries

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 i.e. This abbreviation means "that is to say." When used in the Core, i.e. is limited to the specific examples given. Identity For addition: The number 0; that is N + 0 = N for any number N. For multiplication: The number 1; that is, N x 1 = N for any number N. Identity Element for Addition The number in a set which when added to any number n in the set yields the given number; in general, e is the identity element of addition for a set if n + e = n for all n in the set; the identity element for addition is zero because a + 0 = a and 0 + a= a. Identity Element for Multiplication The number in a set which when any number n in the set is multiplied by, yields the given number; in general, e is the identify element of multiplication for a set if n ae1=1ea=ae = n for all n in the set; the identity element for multiplication is one because a * 1 = 1 * a = a Identity Property of Addition If you add zero to a number, the sum is the same as that number. Example: 7 + 0 = 7. Identity Property of Multiplication If you multiply a number by one, the product is the same as that number. Example: 20 x 1= 20. Image The figure created when another figure, called the pre-image, undergoes a transformation. Impossibility An event that cannot occur in a probability experiment (e.g., rolling the number 7 when tossing a six-sided number cube labeled 1 to 6). This is also known as an impossible outcome. Improper Fraction A fraction whose numerator is greater than its denominator. Inch A customary unit for measuring length or distance; 12 inches = 1 foot; roughly equivalent to the distance from the end of one’s thumb to the first joint. The abbreviation for inch is "in." Incircle A circle that is drawn inside of a triangle that touches all three sides. Income The amount of money received for labor, for services, from the sale of goods or property, or from investments. Increase To become larger in size or quantity. Independent Events Two or more events in which the outcome of one event has no effect on the outcome of the other event or events. Indirect Measurement A process where the measurement of some entity is not obtained by the direct reading of a measuring tool, or by counting of units superimposed alongside or on that entity. For example if the length and width of a rectangle are multiplied to find the area of that rectangle, then the area is an indirect measurement. Indirect Proof The method of proof that assumes the negation of what is to be proved and deduces a contradiction. Inductive Reasoning Making a generalization from specific cases; used to formulate a general rule after examining a pattern. Inequality A relationship between two quantities indicating that one is strictly less than or less than or equal to the other. A mathematical statement containing one of the symbols: >,<,<=, >= or neqto indicate the relationship between two quantities. Infix Notation Symbols used in arithmetic problems. You might find plus, minus, division, and parentheses. Each symbol has a different meaning and different mathematical action. Informally An informal process is not according to prescribed rules. It is a casual process without formal rules. Input Value A value assigned to a variable in a given formula or expression that allows the formula or expression to be evaluated. Example:Evaluate the perimeter of a rectangle given the following input values: L = 12, W = 5 and the formula P = 2L + 2W. Integer A whole number that includes all negative numbers, zero, and all positive numbers. You might have -45, -450,000, 0, 234, or 78,306. Integers do not include decimals or fractions. The set of numbers: {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6,...} Integral Refers to an integer; an integral solution to a problem cannot be a decimal or fraction. Integral Exponent An exponent that is an integer. Example: in the expression 2-1,–1 is the integral exponent of the base number 2. Intercept The points where a line drawn on a rectangular-coordinate-system graph intersect the vertical and horizontal axes. Interest The amount of money charged for borrowing money or the profit (usually money) that is made on invested capital. Interest Rate The percent of interest charged on money borrowed or earned on money invested. Interior Angle An angle on the inside of a polygon formed by two adjacent sides of the polygon. Intersect To meet or cross. Intersecting Lines Lines that share a common point. Intersection of Sets The set of elements that belong to each of two or more sets (e.g., if Set A = {2,4,6,8,10} and Set B = {1,2,3,4,5,6}, then the intersection of sets A and B is {2,4,6}). Interval A set containing all numbers between two given numbers (the endpoints) and one endpoint, both endpoints, or neither endpoint. Invalid An approach or example that is flawed and does not lead to the correct solution of the problem. An invalid approach would be to simplify the expression from left to right, disregarding the order of operations. A valid approach would be to simplify the expression using the order of operations. Inverse For addition: For any number N, its inverse (also called opposite) is a number -N so that N + (-N) = 0 (e.g., the opposite of 5 is -5, the opposite of -3/4 is 3/4). For multiplication: For any number N, its inverse (also called reciprocal) is a number N* so that N x (N*) = 1 (e.g., the reciprocal of 5 is 1/5; the reciprocal of -3/4 is -4/3.) Inverse Operation An operation that is the opposite of, or undoes, another operation; addition and subtraction are inverse operations; multiplication and division are inverse operations. Inverse Property A property of real numbers that states that the result of two real numbers that when combined will result in the identity element; when a number is added to its additive inverse, the sum is always zero; (e.g., 8 + -8 = 0); when a number is multiplied by its multiplicative inverse, the product is always 1. (See additive inverse and multiplicative inverse) Investigate (See explore) Irrational Number A real number that cannot be represented as an exact ratio of two integers. The decimal form of the number never terminates and never repeats. Examples: The square roots of 2 or Pi. Irregular Polygon A polygon whose sides and angles are not all congruent. Irregular Shape (See irregular polygon) Irrelevant Information Extraneous information that has no bearing on the problem and cannot be used in its solution. Example: A DVD player costs \$339.50.Beth has \$550 in her savings account.If she pays \$35 down and one monthly payment of \$22.50, how much more must she pay? Isosceles Trapezoid A trapezoid in which the two nonparallel sides are congruent. Isosceles Triangle A triangle that has exactly two congruent sides (sides of equal length).

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