@Gaudipern@mastodon.gamedev.place
Solo Game Developer, Educator on Break, Un-pixel Artist, Learning Scientist, Chronic Self-Hater.
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While that is what we teach at the lower levels of calculus, that's not actually strictly true. Continuous approximations of discrete systems can be derived to assist in solving the discrete system. This shows up in Taylor Series solutions to square waves, Dirac delta functions for Heaviside step functions and logistic approximations of biochemical/neurological chemical switch-base systems.
(For those who didn't hit that area of math the explanation goes like this:
You cannot derive a discrete function...*
*But you can derive a continuous function whose loss function gets infinitely close to zero when approximating the discrete function, producing an infinitely close answer which may have specific disjoint spots or regions where it is either unsolvable or devolves to infinite solutions but is applicable in all other places.)
