Despite their predictable moderation issues, I still find myself on the Stack Exchange network daily. In the process, I often notice interesting questions from other sites on the network, including this one.
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 remember asking the same question to my year 12 maths teacher, but she shrugged, and I forgot about it. Funny how seeing something years later can trigger all these memories!
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.
It's not often you learn about etymology from a mathematician, but that was the accepted answer. It seems plausible.