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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?

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1 Answer

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They share a Latin root corresponding the the concept of 'wholeness'. In the context of integers, this would be interpreted as 'whole numbers' - i.e. numbers with no fractional part. In the context of integration, this would correspond to 'summing up to create a whole' in the sense of the integral representing a continuous sum or area. I think that's why they use similar words.

I'm no expert in such things, but I've included some links to an online etymology dictionary that appears to agree with me.

1: Integer: From the Latin adjective integer, "whole, complete"
2: Integrate: "to render something whole"/"to put together parts or elements and combine them into a whole"
3: Integral: "of or pertaining to a whole"

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