/tech/ - Soyence and Technology

>>7993 (OP)
>lim
this is a convention not reality.
conventionally we stop caring after a big enough surface area has been bounded.
reality doesn't have any lim. but we can set a convention that
lim 1/n n -> inf = 0
meaning that at some point we stop caring about the almost infinitely small number or let alone able to make a distinction between that extremely small number and 0 that we conventionally decide that both are zero.
lim is found in calculus which is mostly applied to physics and real world which is why it's ok for this part of math to be not as "pure" as say Algebra which is also applied to the real world but doesn't work nearly as much with infinities or approximations

>>7993 (OP)
>>8034
note that we don't claim that math is reality. never was. math is based on a bunch of axims just like arguments are based on a bunch of assumptions (because you need to start somewhere).
thats why we always talk about mathematical "models". because no matter how well you can use math to describe or better approximate reality it'll always be just a more or less accurate model

>>7993 (OP)
Because Ω³ is fine, "take union" and "integrate" commute. So volume = finite limit of finite pieces. But the boundary‐form sheaf j_*Ω² (the pushforward of the boundary 2‑forms along ∂U_R↪U_R (area‑forms)) isn’t fine, so new boundary pieces keep contributing and you cannot collapse them away in the limit, hence infinite surface area.

>>8039
>>8034
how the fuck is gabriel's horn not real doe? pretty sure it can be embedded in a spacetime. Are you implying the real world isn't smooth or what?

meds

>>8108
how do i learn the math needed to understand this post

>>8108
still doesn't make sense

>>8761
first you have to make yourself believe pic related

>>9590
pure schizophrenia, take your meds

>>9139
define your numbers first

Reality>Math

Math tries to replicate reality, not the other way around. Math can go into hypotheticals, but once it crosses that line it's all theoretical.

>>10386
reality=math
prove me wrong

>>11181
You cannot define human language, life forms, phisical entities, etc only with math symbols, thats why we have multiple sciences, one is not reductible to other. If reality is not yet completly understood by all the branches of sciences united neither will be understood only by one branch

>>11181
Go back to reddit.