> > Or I just assert that the function which is defined everywhere except > where there is a removable discontinuity is continuous, and everything > else falls in to place. > > The statement "Let f(t) be a continuous function for all real numbers t" > has a concise meaning.
... for a hypothetical function *assumed* to be properly defined.
With regard to the first statement, I concede that it can be true in certain cases. Here is a good example: