# The word "integral" in calculus unrelated to "integral" / "integer" in algebra?

I think that the word integral in calculus is nothing to do with integer or integer numbers.

But why is integral is chosen for integration? In algebra, integral means related to integers, and this is exactly the same as the word integral in calculus with a very different (?) meaning; are they connected? If not why from millions of words are they same?

• I'm hoping for a better answer than this, but both of these concepts have to deal with the idea of "wholeness". Taken from the entry of integer at dictionary.com "Latin: untouched, hence, undivided, whole =in- in-3 + -teg- (comb. form of tag-, base of tangere to touch) + -er adj. suffix]" Maybe someone can expand on this concept of "wholeness" and how it applies to integrals. It is easy to see how it applies to the word integer. Jul 27, 2015 at 20:02
• Integers are used to count whole things like 3 sacks of wool. 2.5 sacks mean that one sack is not whole. One can make it whole, e.g. if it is only 1/3 full, you may add to it some more wool like another 1/3, then another 1/4 then another 1/12, so that you get the whole sack at the end. 1=1/3+1/3+1/4+1/12 is called integration (making whole from parts). Identical thing happens in calculating an integral (whole) area from small parts (e.g. rectangles).
– A.Γ.
Jul 27, 2015 at 20:46
• This is a weakness of english, too far from latin which made some words collapse into each other. In french instead of integral for calculus, integral for algebra we use integrale for calculus et entier for algebra. Same roots, but very diff words. Entier is also the word for integer, btw. Jul 28, 2015 at 7:49