this post was submitted on 16 Jul 2023
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Which makes the integral sign ∫ a non-discrete for-loop
That does not help. What does non-discrete mean?
Continuous.
Instead of jumping from 1 to 2 to 3, we move smoothly across all (typically real) numbers. Obviously this would go to infinity almost every time because there are infinite real numbers between any two distinct real numbers. So instead, we merge it into a bunch of skinny rectangles with their bottom on the x axis and the top at the value of the function for the start of the rectangle. As we shrink the width of the rectangles, it approaches the continuous notion.
Continuous means “smooth” - there are no jumps Discrete means there are jump