🧵 Untitled Thread
Anonymous at Sat, 19 Oct 2024 11:31:55 UTC No. 16439561
>takes a discrete sum
>takes limit to get integral
>can't calculate integral
>use computer
>computer cannot calculate integral
>discretize integral
>do calculation
>takes finite difference
>takes limit to get derivative
>cannot solve differential equations
>put in computer
>computer cannot solve equation
>discretize differential equations
>do calculation
Why do mathematicians bother with the continuous step that they cannot calculate anyway?
Anonymous at Sat, 19 Oct 2024 15:16:07 UTC No. 16439823
>>16439561
from a purely engineering perspective, the continuum is the approximation to the discrete and not the other way around. it is just much easier to prove theorems, properties, integrals etc on continuous functions when compared to discrete, since many lower order terms go to zero when you take the limit.
Have you seen the discrete version of the FTC relating summations to finite differences? It gets unwieldy for higher order polynomials and I don't even think it is tractable for non-linear functions. In the continuum you don't have that problem because every function is approximately linear with small enough differences and all extra terms go away.
Anonymous at Sat, 19 Oct 2024 15:55:46 UTC No. 16439867
>>16439823
Horrendous post
Anonymous at Sat, 19 Oct 2024 15:58:35 UTC No. 16439874
>>16439561
man, I've grown out of graduate and advanced undergrad analysis and topology because of this. it's just pointless wankery. numerical methods, linear algebra, and other algebras, are just the better investment of resources.
I have no refutation for you, and I loved analysis.
Anonymous at Sat, 19 Oct 2024 21:34:04 UTC No. 16440348
>>16439561
use a physical analog computer for problems hard to reckon on a digital computer bro its easier
Anonymous at Sun, 20 Oct 2024 01:10:29 UTC No. 16440556
>>16439561
>>takes limit to get integral
you fucked up here.