The Nature of Mathematics, 12th Edition
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Glossary - B's

Balinski and Young's Impossibility Theorem Any apportionment plan that does not violate the quota rule must produce paradoxes. And any apportionment method that does not produce paradoxes must violate the quota rule.

Balloon payment A single, larger payment made at the end of the time period of an installment loan that is not amortized.

Bar graph See Graph.

Base (1) See Exponent. (2) In a percent problem, it is the whole quantity.

Base angles In an isosceles triangle, the angles formed by the base with each of the equal sides.

Base b numeration system A numeration system with b elements.

Base of an exponential
In y = bx , the base is b (b not equal to 1).

Base of a triangle In an isosceles triangle, the side that is not the same length as the sides whose lengths are the same.

BASIC Beginner's All-purpose Symbolic Instruction Code; it is a higher-level computer language common to most microcomputers.

Because

Bell-shaped curve See Normal curve.

Belong to a set To be an element of a set.

Bernoulli trial A Bernoulli trial is an experiment that meets four conditions:

  1. There must be a fixed number of trials. Denote this number by n.
  2. There must be two possible mutually exclusive outcomes for each trial. Call them success and failure.
  3. Each trial must be independent. That is, the outcome of a particular trial is not affected by the outcome of any other trial.
  4. The probability of success and failure must remain constant for each trial.

Biconditional A logical operator for simple statements p and q that is true when p and q have the same truth values, and is false when p and q have different truth values.

Billion
A name for 109 = 1,000,000,000

Bimodal A distribution with two modes.

Binary numeration system A numeration system with two numerals, 0 and 1.

Binary voting Selecting a winner by pairing two competitors and then pairing up the winners to select the final victor.

Binomial A polynomial with exactly two terms.

Binomial Distribution Theorem

Binomial Experiment A binomial experiment is an experiment that meets four conditions:

  1. There must be a fixed number of trials. Denote this number by n.
  2. There must be two possible mutually exclusive outcomes for each trial. Call them success and failure.
  3. Each trial must be independent. That is, the outcome of a particular trial is not affected by the outcome of any other trial.
  4. The probability of success and failure must remain constant for each trial.

Binomial Random Variable random variable associated with an experiment having exactly two outcomes.

Binomial theorem

Birthday problem The probability that two unrelated people will have their birthdays on the same day (not counting the year of birth).

Bisect To divide into two equal or congruent parts.

Bit Binary digit, the smallest unit of data storage with a value of either 0 or 1, thereby representing whether a circuit is open or closed.

Bond An interest-bearing certificate issued by a government or business, promising to pay the holder a specified amount (usually $1,000) on a certain date.

Boot To start a computer. To do this the computer must have access to an operating system on a floppy disk or hard disk.

Borda count
A common way of determining a winner when there is no majority is to assign a point value to each voter's ranking.  If there are n candidates, then n points are assigned to the first choice for each voter, with n - 1 points for the next choice, and so on.  The points for each candidate are added and if one has more votes, that candidate is declared the winner. 

Boundary See Half-plane.

Box plot A rectangular box positioned above a numerical scale associated with a given set of data. It shows the maximum value, the minimum value, and the quartiles for the data.

Braces See Grouping symbols.

Brackets See Grouping symbols.

Branch In BASIC programming, a branch is a means of transferring from one point in a program to another under certain conditions. In particular, it refers to the IF-THEN and IF-ELSE commands.

Bug An error in the design or makeup of a computer program (software bug) or a hardware component of the system (hardware bug).

Bulletin boards An online means of communicating with others on a particular topic.

Byte The fundamental block of data that can be processed by a computer. In most microcomputers, a byte is a group of eight adjacent bits and the rough equivalent of one alphanumeric symbol.

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