Index Set

EXAMPLES

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

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

The set

\{f_r\}

(which happens to be a Basis for the Vector Space of all functions on

\mathbb{R}

over

\mathbb{R}

) is an Uncountable Set indexed by

\mathbb{R}

.

SEE ALSO

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