In elementary calculus, continuity and derivatives are painted with the same brush and the brush is called ‘limits’; this is good for showing the core of unity in the processes of calculus. However, when we look at these concepts more closely, they are quite different: continuity has to do with the interaction between functions and open sets, whereas differentiability involves in addition the algebraic structure of the number field (from the very outset one considers ‘difference quotients’).
KeywordsContinuous Function Rational Number Constant Function Inverse Image Neighb Orhood
Unable to display preview. Download preview PDF.