What the fuck does infinitesimally small even mean. Literally how is that possible
What the fuck does infinitesimally small even mean. Literally how is that possible
Just a tiny bit bigger than 0.
Usually you want all arbitrarily small non 0 numbers.
ITS AS SMALL AS POSSIBLE WITHOUT BEING NOTHING SURELY YOU AGREE SUCH A NUMBER MUST EXIST OTHERWISE NO NUMBERS EXIST AT ALL
If you understand infinity you understand infinitesimals.
0.01
0.001
0.0001
0.00001
Ad infinitum
Literally it's impossible to understand infinity
Can't said number just be smaller and smaller. There's no stopping point
It means super duper small. Like, imagine a very small thing, but even smaller. Its like that.
now you understand
AHHHHHHHHHHH
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.
Yeah, this arbitrarily-small, positive number is usually expressed as [math]\epsilon[/math]. This is also the basis for Zeno's paradox.
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.
this
Just look down your pants and you'll find the answer lmao
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.
The function is continuous if and only if this is calculus
>infinitesimally small
It means equal to 0.
This. There's no infinitely small number. Just like .000... = 1.
.000...001 = 0 because it can't exist
.999... = 1 *
Pic related
Me in calc 1.
t. Princeton PhD
>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
it's a concept, not an actual thing
generally it means taking a limit
>.000...001 = 0
0.999... is a repeating decimal though. 0.000...001 has a stopping point
Are you fucking kidding? the ... means infinite. You're saying that you can have a ...001 at the END OF INFINITY?
it doesn't stop until it's finished going on infinitely.
so it doesn't really stop does it?
>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?
>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.
"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.
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
It's the difference between 1 and 0.(9).
Imagine something getting smaller than smaller, expanding in.
>Can't you see that this is a contradiction?
are you incapable of reading two sentences back to back?
It’s a piss poor excuse to show why math works when it really needs new rules.
>Like, imagine a very small thing, but even smaller
Oh, so OPs wee-wee
Delete this