[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 5 KB, 344x108, IMG_20220625_145653.jpg [View same] [iqdb] [saucenao] [google]
15087820 No.15087820 [Reply] [Original]

How can a spike infinitely high have an area of just 1? Shouldn't the area be infinite too?

>> No.15087830

sir, this is a distribution

>> No.15087835

>>15087830
Not such a thing. I have a physics degree and I was taught it is a function

>> No.15087837

>>15087820
Because it is also infinitely narrow. Also that representation of dirac delta is what EE fags are generally using and mathematically not correct.

>> No.15087839

>>15087837
>Because it is also infinitely narrow
Then its area is 0

>> No.15087842

>>15087839
I didn't say its width is zero. I said its infinitely narrow. Do you know the difference between the number '0' and the expression 'lim{x->0}(x)'.

>> No.15087844

>>15087842
If 9.99999999...=10 then lim{x->0}(x)=0

>> No.15087847

>>15087820
>How can a spike infinitely high have an area of just 1?
Take 1x1 square. Make one side 10 times longer and the other 10 times shorter. You have a tall and narrow rectable with the same area. Repeat ad infinitum. You have an infinitely tall, infinitely thin spike with an area of 1.

>> No.15087851
File: 1.10 MB, 375x329, 99F3DF34-42D9-4712-AEDA-0C9EAEA02F44.gif [View same] [iqdb] [saucenao] [google]
15087851

>>15087847
> Take 1x1 square. Make one side 20 times longer and the other 10 times shorter.

>> No.15087855
File: 10 KB, 781x101, delta_fun.png [View same] [iqdb] [saucenao] [google]
15087855

make it finite with some tolerance epsilon, lmao

>> No.15087856

>>15087851
Okay, but then it doesn't have an area of 1 and it's a different object. What point were you trying to make?

>> No.15087859

>>15087847
>Repeat ad infinitum
How do I do this? My life is finite

>> No.15087866

>>15087859
>How do I do this?
Why would you need to "do" it?

>> No.15087870

>>15087866
Because it's one of the steps? If you don't do it infinite times, you'll never get the dirac delta, just a square that is very thin and very tall, but not infinitely tall

>> No.15087871

>>15087859
and oh boy, so is your iq

>> No.15087873

>>15087859
Dude go and take a look at your calculus introduction book. And read the chapter that explains the limits again.

>> No.15087875

>>15087870
why do you want to get a dirac delta? aren't you a physicist?

>> No.15087876

>>15087870
but you obvs don't get the dirac delta

>> No.15087879

>>15087871
>>15087873
Infinites don't exist. Everyone who has claimed he's done a step infinite times is lying. You can't even prove that the limit of x when x tends to 0 is actually 0, because you'd need to do infinite steps to prove it, and nobody has ever done this. It's impossible. If you say you'll get the dirac delta if you do infinite steps, prove it by doing infinite steps. You can't huh? That's why that reasoning is bullshit

>> No.15087886

>>15087870
>If you don't do it infinite times, you'll never get the dirac delta
Math isn't about "doing" anything. An infinitely thin, infinitely tall spike is unambiguously implied by the sequence I gave you as an example.

>> No.15087937

>>15087879
Achilles outruns the tortoise all the time

>> No.15087947

>>15087820
because ∞ * 0 = 1

>> No.15087958

>>15087839
yes and pi is 3

>> No.15087963

>>15087947
interesting

>> No.15087970

>>15087947
22/0 = inf
22 = 0*inf

>> No.15088013

>>15087879

At no point do you need to do an infinite number of steps. Limits are not about exactness, but rather arbitrary precision.

Please review the epsilon-delta definition of a limit.

>> No.15088015

>>15088013
>Limits are not about exactness, but rather arbitrary precision.
Limits are not about "exactness" or "arbitrary precision". Please take the other anon with you and go finish highschool.

>> No.15088017

>>15087855
This is the real answer. Epsilon bullshit makes infinites reasonable.

The Delta Function was added as a physics tool to be able to pull bullshit, but because nature is very accommodating it is fine without rigor.

>> No.15088125

>>15088013
This. People like Norman Wildberger get all fussy over the fact that limiting operations depend on the ability to carry out infinite computations when computers run in a finite time, but fail to realize that the whole idea behind analysis is to accept such limitation and introduce a bit of "fuzz" to at least be able to reason about the truncated computation.

>> No.15088127

>>15088125
105 IQ/pop-sci education take.

>> No.15088130

>>15087820
Infinite length time zero width is indeterminate

>> No.15088232

>>15087820
[math]2 \cdot \infty = \infty [/math] and [math]2 \cdot 0 = 0 [/math] so [math]2 \cdot \delta(x) = \delta (x)[/math].

With this we get
[eqn]1 = \int_{-\infty}^\infty \delta(x) dx = \int_{-\infty}^\infty 2 \cdot \delta(x) dx = 2 \cdot \left( \int_{-\infty}^\infty \delta(x) dx \right) = 2 \cdot 1 = 2 [/eqn]

>> No.15088292

That is just bullshit physicists made up to not learn about measure theory. Use Stieltjes integrals instead.

>> No.15088738

>>15087820
integral of this function is 0

>> No.15088807

>>15087820
>How can a spike infinitely high have an area of just 1? Shouldn't the area be infinite too?

There are lots of well-known mathematical objects that have an infinite perimeter, but a finite area.

For example, if you look at the following area:

- bounded below by the positive X axis
- bounded above by the curve y = 1/x^2
- bounded on the left by the line x = 1
- not bounded on the right

you will see that it has infinite perimeter, but a finite area of 1.

Lots of fractals have this property too, such as the Mandelbrot set and the Koch snowflake.

>> No.15088815

It's a mathematical idealization of some arbitrarily narrow "impulse" with a given integral. It's a useful thing to try to model. I think this kind of idea starts making more sense once you get into measure theory.

>> No.15088825

>>15087820
>spic
shut the fuck up. y'all south american niggers have no business doing math

>> No.15088830

>>15088125
>whole idea behind analysis is to accept such limitation and introduce a bit of "fuzz"

You don't even need to introduce any "fuzz". For example, if you're wondering why the real number 0.9999... is equal to 1, it doesn't take any "fuzz" to prove that the difference between those two numbers cannot contain any non-zero digits, so therefore, by the process of elimination, the difference must contain only 0 digits, and hence, the difference is exactly 0. No truncation of digits is necessary, and no "fuzz" is needed. It's just a straightforward proof by contradiction that takes ALL of the digits into consideration.

>> No.15088849

>>15087820
why couldn't it?

>> No.15088851

>>15087820
It's infinitely narrow.
There are functions that, when rotated around the axis in which they extend infinitely, form a solid with infinite surface but finite volume.
Look up torricelli's trumpet/gabriel's horn.
This will give you a similar idea.

>> No.15088856

>>15088830
What is it about infinities that makes public-highschool-educated midwits come out of the woods and boast their lacking understanding?

>> No.15088859

>>15087847
Take 2x1 square. Make one side 10 times longer and the other 10 times shorter. You have a tall and narrow rectable with the same area. Repeat ad infinitum. You have an infinitely tall, infinitely thin spike with an area of 2.

dirac delta isn't as easily reasoned as you just did, there is nothing inherent about the function that gives it area 1. we just defined it to be like that because it makes life easier in other areas of physics/maths

>> No.15088860

>>15088859
>You have an infinitely tall, infinitely thin spike with an area of 2.
Correct. So what?

>dirac delta isn't as easily reasoned as you just did
My reasoning wasn't for the Dirac delta. It was in direct response to the question an anon posed.

>> No.15088866

>>15088292
this

>> No.15088868
File: 108 KB, 293x314, hmm.png [View same] [iqdb] [saucenao] [google]
15088868

>>15088856
>Cantor was a highschooler

Based schizo now take your meds

>> No.15088872

>>15088868
What does your kiddie-tier post have to do with Cantor, retard? Was it your vague reddit reference to the diagonal argument, which you clearly misunderstood?

>> No.15088875

>>15088856
they don't exist

>> No.15088887
File: 34 KB, 161x175, pot.png [View same] [iqdb] [saucenao] [google]
15088887

>>15088872
Yet another schizophrenic rant misinterpreting me, claiming me being a Redditor, and putting words in my mouth.

Stop projecting your craziness.

Never talk to me again, pic related.

>> No.15088895

>>15088887
You will never be intelligent. You will always be recognize as a redditor.

>> No.15088925

>>15088895
Never talk to me again simpleton of worthless intellect, devourer of brains, demon troll of the worthless depths of intellect, vermin of the conspicuousness and all that is a product of brilliance, satan manifested in the body of a selfish clown throwing his assumptions onto the innocent and the smart.

>> No.15088943

>>15087820
It’s just an impulse bro
>t. EE

>> No.15089002

>>15087835
your degree sucks then, ask for a refund
we covered distributions in our third year

>> No.15089019

>>15089002
And what institution was it that taught you distributions aren't functions?

>> No.15089023

>>15088925
You will never be recognized as an intellectual. You will always be recognized as a redditor.

>> No.15089025

>>15089023
Anyways you are worthless, go do your homework

>> No.15089029

>>15089025
Always a redditor.

>> No.15089033

>>15089029
>Anyone I dislike is a Redditor

You have to cope

>> No.15089038

>>15089033
But you said this site is worse for scientific discussions than reddit in another thread. I know you're a redditor. Why are you lying about it now?

>> No.15089593

>>15087842
there is no mathematical difference, 'lim{x->0}(x)' is a longer way of writing '0'

>> No.15089622

>>15087820
What is the area of a rectangle with zero width and infinite height?

>> No.15090067

>>15089622
zero. trivial question.

>> No.15090070

>>15089622
>a rectangle with zero width and infinite height
What kind?

>> No.15090148

>>15089622
this is not mathematically rigorous since infinity is not a number, it isn't anywhere on the real axis and there are multiple types of infinities of different sizes anyway

>>15090067
this is not true in the calculus sense, it's an undetermined value as stated and varies a lot contextually

think of lim{x->0}(x * 1/(2x + 1)), the first factor, x tends to 0 while the second 1/(2x + 1) tends to infinity, yet the limit converges to 1/2

of course, this is not the same as the parent question since the first factor isn't 0, nor is the second infinity, they are converging functions

>> No.15090158

>>15089622
About the same as the sound of a one-hand clapping.

>> No.15090201

>>15090148
you're retarded

>> No.15090203

>>15088830
But for every 9 you introduce I can determine a minute difference between 1 and your number. Are you talking about a completed infinity or something? It makes sense if we're talking about limits or arbitrary precision but I don't know why you say that they're exactly equal unless you believe it's a complete static object.

>> No.15090272

>>15090203
1/inf=0
once you accept that, the rest is trivial

>> No.15090430

>>15087958
Pi is approximately 3

>> No.15090434

think of the dirac delta "function" as the limit of a normal distribution as the standard deviation approaches zero. Technically the dirac delta function is a distribution, and only really makes sense if it is being integrated.