Absolute value.
The absolute value is defined for real and complex numbers. For real numbers, the absolute value coincides with the number itself if the latter is either positive or zero. The absolute value of a negative number is obtained by multiplying the number by -1, i.e. by changing its sign. The absolute value if a number r is denoted |r|. Therefore, |r|=r for r0 and |r|=-r for negative r. In other words, |r| is the distance form number r to the origin. In this form, the definition applies to complex numbers that are identified with points in the plane.

Abscissa
The first element in a coordinate pair. When graphed in the coordinate plane, it is the distance from the y-axis. Frequently called the x coordinate.

Acute angle
An angle whose measure is between 0o and 90o.

Acute triangle
A triangle with three acute angles.

Algorithm.
The word algorithm comes from the name of a Persian author, Abu Ja'far Mohammed ibn al Khowarizmi (circa 825) who wrote a math textbook. The word refers to a precise prescription (given by a step-by-step description) of a solution to a problem.

Braids Theory.
Braids Theory was invented by Emil Artin and is a part of the Knot Theory. Braids are collections of lines whose ends are attached to two parallel straight lines. There is an interesting puzzle related to the Braids Theory.

Broken-line graph

A type of graph used in data management where the data points are joined by line segments.

Cardinal.
Cardinal numbers were invented by Georg Cantor and generalize the notion of a number of elements to infinite sets. Finite cardinals are just regular non-negative integers. Transfinite cardinals are (often) defined as collections (equivalency classes) of sets that could be put into a 1-1 correspondence with each other. is the first transfinite cardinal and describes the cardinality of denumerable sets, i.e. sets that can be put into a 1-1 correspondence with the set of all integers.

Cardioid.
A special case of epicycloids. A plane curve traced by a point on a circle rolling on the outside of a circle of equal radius.

Cartesian coordinates.
Most often in the plane, but also in the higher dimension spaces, the Cartesian coordinates are defined by a number (2 in the plane) of perpendicular number lines - coordinate axes. A point is then defined by its projections on the axes. In the plane, points are defined by 2 such projections that are written as an ordered pair of real numbers, (x, y).

Cauchy sequence.
A sequence x0, x1, ... of elements of a metric space is said to be a Cauchy sequence if differences |xn+m-xn| are uniformly small in m (i.e. do not depend on m) and tend to 0 as n grows.

Closed interval.
Closed interval is a piece of a straight line that includes its endpoints. On the number line, closed intervals [a,b] are defined as {x: a x b}. Closed intervals are closed sets.

Complementary angles.
Two angles are called complementary is they add up to 90o. E.g. two acute angles in a right triangle are complementary.

Completeness.
There are at least three distinct notions of completeness..

Connected set.
A set that can't be split into a union of two sets each of which is both open and closed.

Consistency.
An axiomatic theory is consistent if it's impossible (in the confines of the theory) to prove simultaneously a statement and its negation. The Godel's Theorem states that any (sufficiently powerful) consistent axiomatic theory is incomplete.

Continuity.
A mapping f:A->B is continuous if images f(a1) and f(a2) of two close points a1 and a2 are also close to each other. This is only meaningful if for both spaces A and B the notion of closeness has been defined. The latter is defined in terms of neighborhoods.

Continuum.
Any set that may be brought into 1-1 correspondence with the set of real numbers. Examples: a finite line segment, a square, a circle, a disk.

Coprime.
Two integers n and m with no common factors are said to be mutually prime or coprime. By definition, gcd(n,m)=1.

Curve.
A curve is a continuous mapping of the segment [0, 1] into another space - container of the curve. A curve may not look as a line. For example, there are space filling curves.