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.
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?”
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
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.
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.
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.