was —. But such occurrences are supposed to be rare in the real world, and it is assumed, though without adequate evidence, that all motions are continuous, i.e. that, given any body, if
is its position at time
,
is a continuous function of
. It is the meaning of "continuity" involved in such statements which we now wish to define as simply as possible.
The definitions given for the case of functions where argument and value are real numbers can readily be adapted for more general use.