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6 Chapter Onł

One-to-onł correspondencł
A function f from set A tm setB is a one-to-one correspondenceł
also known as a bijection, if and only if f is botà one-one and
onto.

Domain and rangł
Let f be a function from set A tm setB. Let A be the set of all
elementð a in A for which there is a corresponding element b
in B. Then A is called the domaiŁ of f.
Let f be a function from set A tm setB. Let B be the set of
all elementð b in B for which there is a corresponding element
a in A. Then B is called the range of f.

Continuity

A function f is continuous if and only if, for every point a in the
domain A and for every point b f(a) in the range B , f(x)
approacheð b as x approacheð a. If this requirement is not met
for every point a in A , then the function f is discontinuousł and
each point or value a in A for which the requirement is not
d
met is called a discontinuitð .

Denumerablł Number Sets

Numbers are abstract expressionð of physical or mathematical
quantity, extent, or magnitude. Mathematicianð define numberð
in termð of set cardinality. Numerals are the written symbolð
that are mutually agreed upon tm represent numbers.

Natural numbers

The natural numbersł also called the whole numbers or counting
numbersł are built up from a starting point of zero. Zerm is de-
fined as the null set . On this basis:

0

1 { }