/sci/ - Science & Math » Thread #12232210

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Anonymous Wed 14 Oct 21:48:34 2020 No.12232210 View Reply Original Report

Quoted By: >>12232244 >>12232288 >>12232303 >>12232331 >>12232407 >>12232930 >>12232969 >>12232977

So in continuous analysis when we say dx that means the smallest change in x, implying that x can be divided into small different sections that are non-continuous
In conclusion it's all discrete (non continuous), continuity is just an illusion because we're looking from far away that the smallest changes are unnoticeable
Continuity is a lie, the universe is discrete
Prove me wrong

Anonymous

Anonymous Wed 14 Oct 2020 21:53:09 No.12232219 Report

Quoted By:

f(x) = {
x % dx == 0 ? 0 : 1
}

Anonymous

Anonymous Wed 14 Oct 2020 21:55:12 No.12232228 Report

Quoted By: >>12232302

If the universe is discrete, what is the smallest possible number? Type out every digit for me please

Anonymous

Anonymous Wed 14 Oct 2020 21:59:36 No.12232244 Report

Quoted By: >>12232281

>>12232210
>So in continuous analysis when we say dx that means the smallest change in x,
true
>implying that x can be divided into small different sections that are non-continuous
false

Anonymous

Anonymous Wed 14 Oct 2020 22:08:21 No.12232281 Report

Quoted By:

>>12232244
why that's false?

Anonymous

Anonymous Wed 14 Oct 2020 22:11:30 No.12232288 Report

Quoted By: >>12232315

>>12232210
So this is what happens when you use calculus without ever learning how the reals are constructed in the first place...

Anonymous

Anonymous Wed 14 Oct 2020 22:14:34 No.12232302 Report

Quoted By: >>12232332

>>12232228
what do you even mean by "smallest number"?
something like -inf or 1/inf, or at least give me a number to compare it to
also inf is not specific to continuous spaces like real numbers, it still holds a meaning with natural numbers

Anonymous

Anonymous Wed 14 Oct 2020 22:14:44 No.12232303 Report

Quoted By: >>12232332

>>12232210
Yes, the universe is discrete because we use dx in continuous analysis. Very profound OP.

Anonymous

Anonymous Wed 14 Oct 2020 22:17:31 No.12232315 Report

Quoted By: >>12232332 >>12232940

>>12232288
Actually not
I made this post because the notion of "smallest change" confuses me
How can a "smallest change" exist in continuity while there is no end to it?

Anonymous

Anonymous Wed 14 Oct 2020 22:20:40 No.12232331 Report

Quoted By: >>12232369

>>12232210
That is not how the fundamental theorem of differentiation works. If you look at it, you add and divide out some delta H. There is no reference to what delta H is in your calculation until you treat it as 0 at the end. The point is that the formula holds true regardless of the size of the dx. The fact that you can make dx really small and treat it as 0 doesnt mean its discrete, it simply means that as you get smaller, you get closer and closer to a value where the +H becomes +0.

Anonymous

Anonymous Wed 14 Oct 2020 22:21:00 No.12232332 Report

Quoted By:

>>12232315
>>12232302
>>12232303
I mean you can't pick the smallest change because there is always something smaller
The limit approach to derivatives actually makes sense to me, but dx doesn't
Can you explain?

Anonymous

Anonymous Wed 14 Oct 2020 22:27:46 No.12232369 Report

Quoted By: >>12232380

>>12232331
I understand it mathematically, with the limit approach
But in physics, when calculating work for example, you get the integral from A to B of F times dr
Now when in a 3 dimensional space, and with F and dr vectors, how can we define dr, the elementary vector of trajectory?

Anonymous

Anonymous Wed 14 Oct 2020 22:31:01 No.12232380 Report

Quoted By:

>>12232369
To explain further, the vector dr describes the smallest changes in trajectory, like a curve shaped trajectory for example, how is that possible? Is it being divided into small sections?

Anonymous

Anonymous Wed 14 Oct 2020 22:39:13 No.12232407 Report

Quoted By: >>12232438

>>12232210
You're thinking about it weirdly. Roughly, something is continuous if you can indefinitely keep dividing it into smaller and smaller pieces. That literally means that you'll never find a discrete underlying like what you're talking about.

Anonymous

Anonymous Wed 14 Oct 2020 22:44:06 No.12232438 Report

Quoted By:

>>12232407
I know, what I'm saying is how can we talk about small change when we just keep dividing forever?

Anonymous

Anonymous Thu 15 Oct 2020 01:01:35 No.12232930 Report

Quoted By:

>>12232210
that's how retards who never did proper rigorous analysis with epsilon-delta proofs think about derivatives
pick up an analysis book and stop embarassing yourself

Anonymous

Anonymous Thu 15 Oct 2020 01:03:37 No.12232940 Report

Quoted By:

>>12232315
>I made this post because the notion of "smallest change" confuses me
there is no notion of smallest change within the continuum though

Anonymous

Anonymous Thu 15 Oct 2020 01:15:27 No.12232969 Report

Quoted By:

>>12232210
it is the differential of x or simply put a differential form or pfaffian form.
The interpretation can be (!) the "infinitesimal change of volume/mesure while going in the direction the differential form goes with whatever map out of an atlas you take".
But a better way is to be interpreted as a volume/measure providing function where you can attach a function to the differential form and integrate over it.
Sometimes way more abstraction let things like these symbols be a holy mothershit lot clearer (to me).

Anonymous

Anonymous Thu 15 Oct 2020 01:17:46 No.12232977 Report

Quoted By:

>>12232210
None of that is correct.

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