e It
is Euler's number and is defined to be the limit of (1 +
1/n)n as n approaches
infinity.
Eccentricity
For a conic section, it is defined as the ratio c/a.
For the ellipse the eccentricity is between 0 and 1 (including
0, but not 1). The eccentricity is the amount of roundness.
If the eccentricity is 0, then the conic is a circle. For
the parabola it is 1 and for the hyperbola it is greater
than 1.
Edge A line or a
line segment that is the intersection of two plane faces
of a geometric figure, or that is in the boundary of a plane
figure.
Either . . .
or
Element One of
the individual objects that belong to a set.
Elementary
operations Refers to the operations of addition,
subtraction, multiplication, and division.
Elementary
row operations There are four elementary row operations
for producing equivalent matrices:
(1) RowSwap Interchange any two rows.
(2) Row+ Row addition; add a row to any other row.
(3) *Row Scalar multiplication; multiply (or divide) all
the elements of a row by the same nonzero real number.
(4) *Row+Multiply all the entries of a row (pivot row) by
a nonzero real number and add each resulting product to
the corresponding entry of another specified row (target
row).
Ellipse The set
of all points in a plane such that, for each point on the
ellipse, the sum of its distances from two fixed points
(called the foci) is a constant.
Elliptic geometry
A non-Euclidean geometry in which a Saccheri quadrilateral
is constructed with summit angles obtuse.
e-mail Electronic
mail sent from one computer to another.
Empirical
probability A probability obtained empirically by
experimentation.
Empty set
See Set.
Encoding key
A key that allows one to scramble, or encode a message.
Encrypt To scramble
a message so that it cannot be read by an unwanted person.
End command
In BASIC, the command that comes at the end of a program.
Equal angles
Two angles that have the same measure.
Equal matrices
Two matrices are equal if they are the same order (dimension)
and also the corresponding elements are the same (equal).
Equal sets
Sets that contain the same elements.
Equal to Two
numbers are equal if they represent the same quantity or
are identical. In mathematics, a relationship that satisfies
the axioms of equality.
Equality,
axioms of
For real numbers a, b, and c:
Reflexive property: a
= a
Symmetric property: If
a = b, then b = a.
Transitive property: If
a = b and b = c, then a = c.
Substitution property: If a = b,
then a may be replaced throughout by b (or
b by a) in
any statement without changing the truth or falsity
of the statement.
Equally likely outcomes
Outcomes whose probabilities of occurring are the same.
Equation A statement
of equality. If always true, an equation is called an identity;
if always false it is called a contradiction. If it is sometimes
true and sometimes false, it is called a conditional equation.
Values that make an equation true are said to satisfy the
equation and are called solutions or roots of the equation.
Equations with the same solutions are called equivalent
equations.
Equation
of a graph Every point on the graph has coordinates
that satisfy the equation, and every ordered pair that satisfies
the equation has coordinates that lie on the graph.
Equation
properties There are four equation properties:
(1) Addition property: Adding the same number to both sides
of an equation results in an
equivalent equation.
(2) Subtraction property: Subtracting the same number from
both sides of an equation
results in an equivalent equation.
(3) Multiplication property: Multiplying both sides of a
given equation by the same
nonzero
number results in an equivalent equation.
(4) Division property: Dividing both sides of a given equation
by the same nonzero
number results
in an equivalent equation.
Equilateral
triangle A triangle whose three sides all have the
same length.
Equilibrium
point A point for which the supply and demand are
equal.
Equivalent
equations See Equation.
Equivalent
matrices Matrices that represent equivalent systems.
Equivalent sets
Sets that have the same cardinality.
Equivalent
systems Systems that have the same solution set.
Estimate An
approximation (usually mental) of size or value used to
form an opinion.
Euclidean
geometry The study of geometry based on the assumptions
of Euclid. These basic assumptions are called Euclid's postulates.
Euclid's postulates
1. A straight line can be drawn from any point to any other
point.
2. A straight line extends infinitely in either direction.
3. A circle can be described with any point as center and
with a radius equal to any finite
straight line drawn from the center.
4. All right angles are equal to each other.
5. Given a straight line and any point not on this line,
there is one and only one line through
that point that is parallel to the
given line.
Euler circles
The representation of sets using interlocking circles.
Euler circuit
Begin at some vertex of a graph, travel on each edge exactly
once, and return to the starting vertex. The path that is
a trace of the tip is called an Euler circuit.
Euler circuit
theorem Every vertex on a graph which is an Euler
circuit has an even degree, and conversely, if in a connected
graph every vertex has an even degree, then the graph is
an Euler circuit.
Euler's number
It is the number e .
Evaluate To
evaluate an expression means to replace the variables by
given numerical values and then simplify the resulting numerical
expression. To evaluate a trigonometric ratio means to find
its approximate numerical value. To evaluate a summation
means to find its value.
Even vertex
In a network, a vertex with even degree; that is, with an
even number of arcs or line segments connected at that vertex.
Event A subset
of a sample space.
Exact interest
The calculation of interest assuming that there are 365
days in a year.
Exact solution
The simplified value of a logarithmic expression before
approximation by calculator.
Exclusive or
A translation of p or q which includes p or
q, but not both. In this book we translate the exclusive
or as "either p or q ."
Expand To simplify
by carrying out the given operations.
Expand a summation
To write out a summation notation showing the individual
terms without a sigma.
Expanded notation
A way of writing a number that lists the meaning of each
grouping symbol and the number of items in that group.
For example, 382.5, written in expanded notation is
3 x 102 + 8 x 101 + 2 x 100
+ 5 x 10-1
Expectation See Mathematical
expectation.
Expected value
See Mathematical expectation.
Experiment
An observation of any physical occurrence.
Exponent
Where b is any nonzero real number and n
is any natural number, the exponent is defined as follows:
bn = bbb ... b
(n factors)
b0= 1
b-n = 1/bn
b is called the base, n is called
the exponent, and bn is called
a power or exponential.
Exponential See Exponent.
Exponential
curve The graph of an exponential equation. It indicates
an increasingly steep rise, and passes through the point
(0, 1)
Exponential
equation
An equation of the form y = bx where b
is positive and not equal to 1.
Exponential function
A function that can be written as f (x)
= bx where b is positive and not equal
to 1.
Exponential notation
A notation involving exponents.
Exponentiation
The process of raising a number to some power.
See Exponent.
Expression
Numbers, variables, functions, and their arguments that
can be evaluated to obtain a single result.
Extended
order of operations 1. First, perform any operations
enclosed in parentheses.
2. Next, perform any operations that involve raising to
a power.
3. Perform multiplications and divisions as they occur by
working from left to right.
4. Finally, perform additions and subtractions as they occur
by working from left to right.
Exterior angle
An exterior angle of a triangle is the angle on the other
side of an extension on one side of the triangle.
Extraneous root
A number obtained in the process of solving an
equation that is not a root of the equation to be solved.
Extremes See
Proportion.
