/tech/ - Soyence and Technology

>>7863 (OP)
There's literally zero dogma on math, you pick your own axioms and make your own system if you want, no one is preventing you to.

>>7865
>>7863 (OP)
technically yes we should write ~ instead of =
lim(1/n) n-> 1 ~ 1
but if we talking about
>>7865
I think he means conventions which higher math is indeed full of.

>>8011
>lim(1/n) n-> 1 ~ 1
better example lim(1/n) n->inf = 0

>>7865
there's doctrine in math though https://ncatlab.org/nlab/show/doctrine

what if it wasnt 1 though?

Deepseek has generated a really good answer for this

>>8605
the reality is that higher math doesn't seek truth but a consistent system that is a system without contradictions which is why you end up with stuff like 0.999… = 1
any child can see that this isn't true but for the sake of keeping the system alive we have to define/agree on this being true so yes op is 100% correct on it being a dogma

>>8606
it's obviously true you fucking retard

>>8865
>stop giving me cognitive dissonance for accepting something as true that everyone with common sense will see as obviously wrong
part of higher math education or rather indoctrination is making you believe stuff like this without questioning it so I don't blame you

>>9047
again, you don't understand even the basics of analysis. You'd also claim different adic representations of some real numbers wouldn't be the same number

>>9048
my point is higher math especially analysis is a construct and not truth. So stating things like in OP like it's truth is misleading.
The only claim to validity OPs pic has is that it's relatively true to the construct of analysis/higher math but it's objectively false in the objective reality. In reality there's no such thing as 0.999…=1
go ask anyone on the street and present the pic in OP they'll laugh at you
the truth is that you made yourself believe it's true out of conformity and necessity.
you're in for a rude awakening once you accept this fact

>>9054
and again, you are a fucking retard. None of the axioms mathematicians work with are arbitrary, in fact, they are so natural most mathematicians abide by them despite not even knowing them. And then, in actual higher math, you go well beyond these "arbitrary" axioms (e.g. Grothendieck-Universes, defining infty-categories, etc.) because it's just natural to do so (a cochain complex of abelian groups lives naturally in an infty-cat, the homotopy type of a space is fully captured by a infty-groupoid, etc.).
It's quite literally a process of discovery. Do more math

>>7863 (OP)
how is it dogma if you can prove it?

>>8606
>he reality is that higher math doesn't seek truth but a consistent system
yes
>any child can see that this isn't true
no

if you can make both these statements, you fundamentally misunderstand what math even is

or perhaps you stopped studying math after learning arithmetic and integers, and you've elevated arithmatic to the level of a divine ontology of reality, verses calculus which is just an internally consistent system.

>>9796
retard

>>8509
If it's not 1, then you should be able to tell me the digit in between 0.999… and 1. You won't/can't so you just have to accept the soyence and agree that 0.999… is another notation for 1.

>>11216
*digit->number

>>7863 (OP)
why does this make first semester university student feel so smart?