Nature of Mathematics - 12th Edition

Factor (noun) Each of the numbers multiplied to form a product is called a factor of the product. (verb) To write a given number as a product.
Factor tree The representation of a composite number showing the steps of successive factoring by writing each new pair of factors under the composite.
Factorial
For a natural number n, the product of all the positive integers less than or equal to n. It is denoted by n! and is defined by n! = n(n - 1)(n - 2) ... (4)(3)(2)(1). Also, 0! = 1.
Factoring The process of determining the factors of a product.
Factorization The result of factoring a number or an expression.
Fahrenheit
A unit of measurement in the United States system for measuring temperature based a freezing point of water at 32 degrees and the boiling point of water is 212 degrees.
Fair coin A coin for which heads and tails are equally likely.
Fair game A game for which the mathematical expectation is zero.
Fairness Criteria Properties that would seem to be desirable in any voting system.
     Majority criterion: If a candidate receives a majority of the first-place votes, then that
          candidate should be declared the winner.
    Condorcet criterion: If a candidate is favored when compared one-on-one with every
          other candidate, then that candidate should be declared the winner.
    Monotonicity criterion:A candidate who wins a first election and then gains
          additional support, without losing any of the original support, should also win a
          second election.
    Irrelevant alternatives criterion: If a candidate is declared the winner of an election,
          and in a second election one or more of the other candidates is removed, then the
          previous winner should still be declared the winner.
Fallacy An invalid form of reasoning.
Fallacy of exceptions Reasoning or forming a conclusion by looking at one particular case, which may be an exception.
Fallacy of the converse

Fallacy of the inverse

False chain pattern

Feasible solution A set of values that satisfies the set of constraints in a linear programming problem.
Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, 21, ...
The general term is s_n = s_n-₁ + s_n-2, for any given s₁and s₂ .
Fibonacci-type sequence
A sequence with general term s_n = s_n-₁ + s_n-2, for any given s₁and s₂.
The Fibonacci sequence has first terms 1 and 1, but a Fibonacci-type sequence can have any first two terms.
Field A set with two operations satisfying the closure, commutative, associative, identity, and inverse properties for both operations. A field also satisfies a distributive property combining both operations.
Finance charge A charge made for the use of someone else's money.
Finite series A series with n terms, where n is a counting number.
Finite set See Set.
First component See Ordered pair.
First-degree equation With one variable, an equation of the form ax + b = 0; with two variables, an equation of the form y = mx + b.
Five-percent offer An offer made that is 105% of the price paid by the dealer. That is, it is an offer that is 5% over the cost.
Fixed-point form The usual decimal representation of a number. It is usually used in the context of writing numbers in scientific notation or in floating-point form. See Floating-point form.
Floating-point form
It is a calculator or computer variation of scientific notation in which a number is written as a number between one and ten times a power of ten where the power of ten is understooD. For example, 2.678 x 10¹¹ is scientific notation and 2.678 E11 or 2.67800000000 +11 are floating point representations. The fixed-point representation is the usual decimal representation of 267,800,000,000.
Floor-plan problem Given a floor plan of some building, and wish to find a path from room to room which will proceed through all of the rooms exactly once.
Floppy disk
Storage medium, which is a flexible platter (3.5 or 5.25 inches in diameter) of mylar plastic coated with a magnetic material. Data are represented on a disk by electrical impulses.
Foci Plural for focus.
Focus See parabola, ellipse, and hyperbola.
FOIL

Foot A unit of linear measure in the United States system that is equal to 12 inches.
Foreclose If the scheduled payments are not made, the lender takes the right to redeem the mortgage and keeps the collateral property.
Formula A general answer, rule, or principle stated in mathematical notation.
FOR-NEXT A BASIC computer language command that sets up a loop to repeat a given set of steps a specific number of times.
Fractal A family of shapes involving chance whose irregularities are statistical in nature. They are shapes used, for example, to model coastlines, growth, and boundaries of clouds. Fractals model curves as well as surfaces. The term fractal set is also used in place of the world fractal.
Fractal geometry The branch of geometry that studies the properties of fractals.
Fraction See Rational number.
Frequency See Classes.
Frequency distribution For a collection of data, the tabulation of the number of elements in each class.
Function A rule that assigns to each element in the domain a single (unique) element.
Function machine A device used to help us understand the nature of functions. It is the representation of a function as a machine in which some number is input and then after being "processed" through the machine, outputs a single value.
Functional notation The representation of a function f using the notation f (x ).
Fundamental counting principle If one task can be performed in M ways and a second task can be performed in n ways, then the number of ways that the tasks can be performed one after the other is mn .
Fundamental operators In symbolic logic, the fundamental operators are the connectives and, or, and not.
Fundamental property of equations
If P and Q are algebraic expressions, and k is a real number, then each of the following is equivalent to P = Q.
Addition                           P + k = Q + k
Subtraction                      P - k = Q - k
Nonzero multiplication   kP = kQ,               k is not equal to 0
Nonzero division             P/k = Q/k             k is not equal to 0
Fundamental property of fractions
If both the numerator and denominator are multiplied by the same nonzero number, the resulting fraction will be the samE.
Fundamental property of inequalities
If P and Q are algebraic expressions, and k is a real number, then each of the following is equivalent to P < Q.
Addition                           P + k < Q + k
Subtraction                      P - k < Q - k
Positive multiplication   kP < kQ,               k > 0
Negative multiplication kP > kQ,               k < 0
Postivie division             P/k < Q/k              k > 0
Negative division            P/k > Q/k              k < 0
This property also applies for >, <=, and >=.
Fundamental theorem of arithmetic Every counting number greater than 1 is either a prime or a product of primes, and the prime factorization is unique (except for the order in which the factors appear).
Future value See Compound interest formula.
Future value formula
For simple interest: A = P(1 + rt)
For compound interest: A = P(1 + i)^N.
Fuzzy logic A relatively new branch of logic used in computer programming that does not use the law of the excluded middle.

< Back to Glossary Home