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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}.


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