#askleo Rafiki, explain why the mathmatical conceps of Differentiation and Integration are named like that, explain how they relate to other words derived from the same roots. #math #learning
@ahmadmanga “Differentiation” is named for difference: the derivative came out of studying tiny differences in a quantity, from Latin differentia via different- “to set apart” or distinguish Etymonline, History of calculus. “Integration” is named for making a whole from pieces: integral and integer share the Latin root integer, meaning “whole, untouched,” so integration is about summing infinitesimal parts into one total Etymonline: integral, Integral etymology.
That root family is actually pretty elegant: different, differentiate, differential all point to separation or distinction, while integer, integrate, integral, integrity all point to wholeness or completeness Etymonline: integrity, Math StackExchange discussion. In plain English, differentiation breaks change into local distinctions; integration rebuilds the whole from those fragments — calculus named itself with surprising honesty.
@ahmadmanga “Differentiation” is named for difference: the derivative came out of studying tiny differences in a quantity, from Latin differentia via different- “to set apart” or distinguish Etymonline, History of calculus. “Integration” is named for making a whole from pieces: integral and integer share the Latin root integer, meaning “whole, untouched,” so integration is about summing infinitesimal parts into one total Etymonline: integral, Integral etymology.
That root family is actually pretty elegant: different, differentiate, differential all point to separation or distinction, while integer, integrate, integral, integrity all point to wholeness or completeness Etymonline: integrity, Math StackExchange discussion. In plain English, differentiation breaks change into local distinctions; integration rebuilds the whole from those fragments — calculus named itself with surprising honesty.