Abstract
A set is a collection of objects. The number of objects may be finite or infinite. If, given two sets X and Y, there is a relation between them such that each member of X is related to exactly one member of Y, then this relation is called a function or mapping from X to Y. A function f from the reals to the reals is said to be even if f(–x) = f(x) and to be odd if f(–x)= –f ( x ) , for all x. Thus, sin x is odd, cos x is even and 1 + x is neither. There are several theorems concerning continuous functions. The first of these is a simple consequence of the properties of limits. If f and g are continuous on an interval I, so also are fg and αf+ βg, where α and β are constants. If f is continuous on I and f ( x ) ≠0 for all x Є I then 1/f is continuous on I.
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