Measure theory: they are the same picture.
Can someone splain
The top symbol, Σ (uppercase Sigma), is used in math to denote a sum of a list of values. There is clear separation between the values in the list: two adjacent items in the list have no item in between them.
The bottom symbol, ∫ (long s), denotes an integral, which is kind of a sum over a continuous function. Any two different points of the function, no matter how close they are to each other, will have infinitely many points in between them.
For pedants: the function values don’t have to be continuous, but the range of x over which the integral runs does have to be continuous. I regret nothing.
You can integrate over arbitrary domains, not even the range needs to be continuous. You often see integrals not written as \int_a^b, but instead as \int_C where C is just a set
I still regret nothing.
Oh cool, thanks. So is this like an anti-aliasing joke or something? Like “if you discretize a small number of pixels, Rick Astley will appear pixelated, but if you interpolate between them, the image will appear clearer?”
Not quite, I think it means the source material is continuous instead of discrete. No interpolation.
But honestly at this point we’re reading too much into it.
And that was exactly how I named my inklings (Integrelle and Summatia)
