Index Set

EXAMPLES

An Enumeration of a set ''S'' gives an index set $J \sub \mathbb{N}$ , where $f:J
arr \mathbb{N}$ is the particular enumeration of ''S''.

For $r \in \mathbb{R}$ , the Indicator Function on r, is the function $\mathbf{1}_r\colon \mathbb{R}
arr \mathbb{R}$ given by

\mathbf{1}_r (x) := \begin{cases} 0, & \mbox{if }  x 
e r  \ 1,  & \mbox{if } x = r. \end{cases}

The set of all the

\mathbf{1}_r

functions is an Uncountable Set indexed by

\mathbb{R}

.

SEE ALSO

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