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/sci/ - Science & Math


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File: 48 KB, 350x494, 1595960099582.png [View same] [iqdb] [saucenao] [google]
11955808 No.11955808[DELETED]  [Reply] [Original]

Checkmate .999...=/=1 tards

>> No.11955815

>>11955808
I honestly don't even understand this...

>> No.11955822

>>11955808
This is evidence of the opposite though. If you approach something for an infinite amount of time, by definition you will never arrive there.

>> No.11955824

>>11955815
Oh no I get it now, I think. What are pictures even? Math is numbers.

>> No.11955851

I feel like this would converge to a larger circle than the blue one. It's like the "extra space" between the square and the circle is becoming more evenly distributed along the whole circle, until it's totally around it and you just have a circle around a slightly smaller circle.

>> No.11955852

>>11955851
I mean, you're clearly losing area but if you imagine these shapes as being made of string I guess I mean the "extra string". This isn't actually a statement, it's some sort of am appeal to intuition, and my intuition tells me you would get a bigger circle

>> No.11955856

This example would actually be a pretty interesting way to ease into the intuition behind fractal dimensions.

>> No.11955857

>>11955808
convergence of functions, even uniform, doesn't imply convergence of derivatives

>> No.11956724
File: 51 KB, 570x409, 1-Bucky-1.jpg [View same] [iqdb] [saucenao] [google]
11956724

>>11955808
based

>> No.11956744

>>11955857
can you elaborate

>> No.11956751

>>11955808
wtf is this real?

>> No.11956759
File: 35 KB, 563x523, 1583448681933.jpg [View same] [iqdb] [saucenao] [google]
11956759

>>11955808
the image implies an integration techniques is used but if we look at a quarter of the circle we can see that the cuts that'd represent dx are not equal and for a true integral they need to be equal otherwise you lose precision

>> No.11956806

>>11956751
The length of a (piecewise differentiable) curve is computed by integrating the norm of the tangent vector (this is called arc length). The important thing is that the tangent vector is just the first derivative. In general, convergence of functions doesn't imply convergence of derivatives, therefore there's nothing contradictory about a convergent sequence of curves such that length of the limit curve is not the limit of the lengths.

>> No.11956817
File: 11 KB, 666x978, √2=2.gif [View same] [iqdb] [saucenao] [google]
11956817

>> No.11956846
File: 10 KB, 618x175, Slope Proof .999...≠ 1.png [View same] [iqdb] [saucenao] [google]
11956846

>>11955857
>convergence of functions, even uniform, doesn't imply convergence of derivatives

That's right. Therefore you CAN'T assume that a series such as:
.9
.99
.999
.9999
.99999

...will have 1 as its conclusion. There simply is no "conclusion" to this, just like there is no "last nine" at the end of .999...

Pictured: Line BW has a slope of 0. Line BZ has an infinitesimal slope. They are clearly different lines that arrive at different points, and only intersect at 0,0.

>> No.11956848

What about 1 - ε?

>> No.11956851

>>11956846
>Therefore
lol try harder you sad schizo

>> No.11956863

>>11956851
Content-free insults are the closest you get to an admission of defeat on 4chan.

>> No.11956873

>>11955852
Mah man!

>> No.11956883

>>11955808
The curve being described here isn't actually a circle, it's a fractal which encloses an area of 0.25*pi and has a finite perimeter length of four. If you have a constraint that your curve must have a perimeter of four like in the second panel, you can construct any arbitrary closed curve which encloses an area of pi*(2/pi)^2, i.e. a circle of radius 2/pi or ~0.64. Here, the radius is 0.5. What is impossible, is using a curve of perimeter length four to enclose an area greater than ~1.27.

>> No.11956892

>>11955851
>I feel like this would converge to a larger circle than the blue one.

I don't see it that way. Each corner removed has a point defined as being on the circle. So once you have removed an infinite number of points, every remaining point on your shape is on the circle, therefore it IS the circle.

>> No.11956898

>>11956883
>The curve being described here isn't actually a circle, it's a fractal which encloses an area of 0.25*pi and has a finite perimeter length of four.

Neither shape has any points that the other does not. Yet somehow it is not the same shape?

>> No.11956902

>>11955808
There's actually way more retards than I thought on /sci/

>> No.11956915
File: 75 KB, 394x500, piequals3root3.jpg [View same] [iqdb] [saucenao] [google]
11956915

>>11956898
I looked it up, and oh shit, I'm wrong! But the perimeter of the final curve isn't four- it's 3.14159 like normal math would say.

https://qntm.org/trollpi

"The limit of a sequence isn't necessarily a member of that sequence.

Because of this, the limit of a sequence need not necessarily share any properties with the members of that sequence."

>> No.11956918

>>11956848
how do you define epsilon?

>> No.11956921

let A(x,y,n) be the sequence enclosing the circle.

in this case lim(n->inf) lenght(A(x,y,n))=4 but lenght( lim(n->inf) A(x,y,n) ) =pi.

It is just a case when you cannot naively interchange operators.

>> No.11956929

>>11956759
intentionally bad picture. i respect that.

>> No.11957061

>>11956915
>https://qntm.org/trollpi

Consider the following series:

4, 4, 4, 4, 4, 4, 4, 4, 4...

Calculate it's limit.

>> No.11957090

>>11957061
not a series

>> No.11957136

>>11957090
sure it is, retard
sum{4,0,0,...}

>> No.11957147

>>11957090
Consider the following series:

Sum(4+0*n) for n 1 to inf

Calculate it's limit

>> No.11957151

>>11957147
oops, you're a retard too

>> No.11957190

>>11957136
not a series

>> No.11957197

>>11957190
>brainlet.jpg

>> No.11957206

>>11957197
>curly brackets
>implying order doesn't matter

>> No.11957211

>>11957206
>crying_brainlet.jpg
cope

>> No.11957217

>>11957211
>I have no argument

>> No.11957225

>>11957217
lol no shit

>> No.11957467

>>11956846
>some shit about derivatives
>therefore some shit unrelated to derivatives
desperate
>they are clearly different
>implying i should trust your picture is accurate

>> No.11957487

>>11956846
i like this, but "Limit" Z isn't a point on the plane. it has no real x coordinate