Page 26 - DMTH401_REAL ANALYSIS

Real Analysis

Notes A mathematical development of the number systems is depicted in Figure 1.6:
Figure 1.6: A Mathematical Development of Numbers Systems

 We have discussed the geometrical representation of the real numbers and stated the
continuum Hypothesis. According to this, every real number can be represented by a
unique point on the line and every point on the line corresponds to a unique real number.
In view of this, we call this line as the Real Line.
1.7 Keywords

Constant Function: Let S and T be any two non-empty sets. A function f: ST defined by
f(x) = c, for each x in S, where c is fixed element of T, is called a constant function.
Co-domain: The set S is called the domain of the function f and T is called its co-domain.
Finite: A set with a limited number of elements is a Finite set.

Function: A function f: ST is a rule by which you can associate to each element of S, a unique
element of T.

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