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/sci/ - Science & Math


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9474280 No.9474280 [Reply] [Original]

What the fuck does infinitesimally small even mean. Literally how is that possible

>> No.9474282

>>9474280
Just a tiny bit bigger than 0.
Usually you want all arbitrarily small non 0 numbers.

>> No.9474283

>>9474280
ITS AS SMALL AS POSSIBLE WITHOUT BEING NOTHING SURELY YOU AGREE SUCH A NUMBER MUST EXIST OTHERWISE NO NUMBERS EXIST AT ALL

>> No.9474284

>>9474280
If you understand infinity you understand infinitesimals.

>> No.9474286

0.01
0.001
0.0001
0.00001
Ad infinitum

>> No.9474287

>>9474284
Literally it's impossible to understand infinity

>> No.9474290

>>9474282
Can't said number just be smaller and smaller. There's no stopping point

>> No.9474294

>>9474280
It means super duper small. Like, imagine a very small thing, but even smaller. Its like that.

>> No.9474295

>>9474287
now you understand

>> No.9474299

>>9474294
AHHHHHHHHHHH

>> No.9474306

>>9474290
Yep, that's why you talk about neighborhoods, as epsilon. That way, you're looking at all of them. Usually. Sometimes, like with discontinuity you only need to show one neighborhood exists.

>> No.9474560

>>9474290
Yeah, this arbitrarily-small, positive number is usually expressed as [math]\epsilon[/math]. This is also the basis for Zeno's paradox.

>> No.9474567

>>9474290
>>9474560
If you're interested in this sort of thing, Arthur Mattuck's "Introduction to Analysis" is a great first-exposure to the topic. It gives the reader and intuition for the subject, without being overly autistic about the rigor too early on.

>> No.9474577

>>9474294
this

>> No.9474690

>>9474280
Just look down your pants and you'll find the answer lmao

>> No.9474999

Don't bother about it. Modern analysis uses the epsilon-delta definition. There are no infinitesmals anywhere unless you specifically seek out non-standard analysis.

>> No.9475014

>>9474280
>>9474282
The function is continuous if and only if this is calculus

>> No.9475079

>>9474280
>infinitesimally small
It means equal to 0.

>> No.9477311

>>9475079
This. There's no infinitely small number. Just like .000... = 1.
.000...001 = 0 because it can't exist

>> No.9477314
File: 106 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google]
9477314

>>9477311
.999... = 1 *
Pic related

>> No.9477359

>>9474280
Me in calc 1.

>> No.9477361

>>9474294
t. Princeton PhD

>> No.9477363
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9477363

>>9474280
>What the fuck does infinitesimally small even mean.
It's in reference to what is called the [math]\varepsilon-\delta[/math] proof. This is what you learn about on the first day of the first semester of calculus

>> No.9477375

it's a concept, not an actual thing
generally it means taking a limit

>> No.9477497

>>9477311
>.000...001 = 0
0.999... is a repeating decimal though. 0.000...001 has a stopping point

>> No.9477512

>>9477497
Are you fucking kidding? the ... means infinite. You're saying that you can have a ...001 at the END OF INFINITY?

>> No.9477513

>>9477497
it doesn't stop until it's finished going on infinitely.
so it doesn't really stop does it?

>> No.9477535

>>9477512
>You're saying that you can have a ...001 at the END OF INFINITY?
I'm implying the opposite you fucking brainlet. What kind of decimal repeats forever and has a stopping point?
>>9477513
>it doesn't stop until it's finished going on infinitely.
Can't you see that this is a contradiction? Nothing stops when it goes on for infinity, by definition.

>> No.9477553

"Infinitesimally small" is a trick used in calculus to obtain a ratio without suffering from "division by zero".
The slope of a curve is obtained by dividing the Y-difference between two points on the curve by the X-difference between them. As long as the points remain separated there will be protests that you've not gotten the slope AT the given point. Infinitesimals allow you to get the points so close together that the error vanishes.

>> No.9477555
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9477555

>>9477535
Oh yeah I read your post wrong.
but I said
>.000...001 = 0 because it can't exist
So you read my post wrong too. BRAINLET

>> No.9477575

>>9474280
It's the difference between 1 and 0.(9).
Imagine something getting smaller than smaller, expanding in.

>> No.9477600

>>9477535
>Can't you see that this is a contradiction?
are you incapable of reading two sentences back to back?

>> No.9477619

It’s a piss poor excuse to show why math works when it really needs new rules.

>> No.9477716
File: 56 KB, 408x491, 1498986701466-sci.jpg [View same] [iqdb] [saucenao] [google]
9477716

>>9474294
>Like, imagine a very small thing, but even smaller
Oh, so OPs wee-wee

>> No.9477763
File: 107 KB, 1280x785, IMG_0402.jpg [View same] [iqdb] [saucenao] [google]
9477763

>>9477716
Delete this