Re: terminology in definitions of limits

["mail.btinternet.com" <ronnie.profbrown@btinternet.com>]

Without getting into discussion of the `game' aspect, I feel category
theorists should speak out against the epsilon-delta approach to limits as
against the neighbourhood
                       f(M) \subseteq N
approach, where the notation easily describes  the pictures. The
epsilon-delta approach is in terms of measurement of a neighbourhood, i.e.
one step away from the neighbourhood, and less actual (I almost wrote
`real'!), and students find that step difficult.  The utility of
epsilon-delta is in terms of calculation, rather than geometry and
structure.

The  `only measurable things are real' approach is based on the notion that
numbers are the most important aspect of science, rather than one tool to
investigate  structure.

Ronnie