/sci/ - Science & Math

[Anonymous No.9562242]

What does 'infinitesimally small' mean? i keep seeing anons on here saying that 0.000...01 does not exist.

[Anonymous No.9562246]

>>9562242
0.000...02

[Anonymous No.9562251]

>>9562242
It means "so small, it loses value in reference to something"
1 meter is infinitesimally small compared to a galaxy, but not small at all to an ant.

[Anonymous No.9562256]

>>9562251
wouldnt that make

(f(x + (delta(h))) - f(x))/h = derivative

invalid?

[Anonymous No.9562275]

>>9562242
0.0000...01 = 0

10^-50 ≈ 0 (unless multiplying or dividing)

[Anonymous No.9562320]

>>9562256
Not at all. Delta x becomes so small compared to f(x), that it effectively becomes zero. And when you use the definition of a derivative like you wrote down, the delta x is cancelled out, giving you your derivative.

[Anonymous No.9562328]

It means decimal accuracy above 16 decimal places. At that point the fraction is so small it doesnt matter.

[Anonymous No.9562353]

>>9562328
[math]\frac{1}{10} = 0.1 \\ \frac{1}{100} = 0.01 \\ \frac{1}{1,000} = 0.001 \\ \frac{1}{10,000} = 0.0001 \\frac{1}{100,000} = 0.00001 \\ \frac{1}{1,000,000} = 0.000001 \\ \frac{1}{10,000,000} = 0.0000001 \\ \frac{1}{100,000,000} =
0.00000001 \\ \frac{1}{1,000,000,000} =
0.000000001 \\ \frac{1}{10,000,000,000} = 0.0000000001 \\ \frac{1}{100,000,000,000} = 0.00000000001 \\ \frac{1}{1,000,000,000,000} = 0.000000000001 \\ \frac{1}{10,000,000,000,000} = 0.0000000000001 \\ \frac{1}{100,000,000,000,000} = 0.00000000000001 \\ \frac{1}{1,000,000,000,000,000} = 0.000000000000001 \\ \frac{1}{\infty} = 0.0000000000000001 [/math]

[Anonymous No.9562382]

>>9562242
Think infinitely big, but the opposite of that

[Anonymous No.9562475]

>>9562242
if \forall \epsilon > 0 , d(x,y) < \epsilon \implies x and y are "same"

[Anonymous No.9562496]

>>9562353
Crazy thing about that typo is that it shows you typed that whole thing out by hand.

This is the level of free time your average /sci/ shitposter has on their hands.

[Anonymous No.9562511]

>>9562328
>t. Engineer

[Anonymous No.9562974]

>>9562382
what's the opposite of my cock?

[Anonymous No.9563011]

>>9562974
your brain

[Anonymous No.9563093]

>>9562242
Infinitely small = 0
Here's a challenge: walk one meter at a constant rate in an infinite time period. To do this, the theoretical answer is to walk an infinitely small distance per second. However, any progress made guarantees that you will eventually walk one meter, so the practical solution is to not move at all. So infinitely small in theory is equal to zero in application.

[Anonymous No.9563181]

>>9563093
looks like someone doesn't know the difference between surely and almost surely.

[Anonymous No.9563197]

>>9562242
It means nothing. 0 to be exact.
[eqn]
\lim_{x\to\infty}\frac{1}{x}=0
[/eqn]

[Anonymous No.9563261]

>>9562242
0.000...01 does not exist in the way you might think it does. it is a fiction that comes from not understand decimal representations.

if you think that you can write an infinite number of 0 digits after a decimal point and then just write a 1 digit, then that's impossible: you used up your infinity when you wrote the zeroes and now you have no more room. if you want to put a 1 somewhere in that expansion, you have to pick a specific place value in which to do it---tenths? hundredths? thousandths? googolths?---and once you do that you have irreparably made yourself strictly greater than zero. you can't get infinitely close to a number unless you are that number already.

"but then why can we write .999...? shouldn't it be the same on both sides?" you might ask. well, with .999..., you're just putting a 9 in every place value, so you're not overstepping your bounds and trying to write something you can't write.

the fact that .999... is equal to 1, and that decimal representations are not unique, is a relevant discussion now, but that requires some arithmetic. the nonexistence of ".000...01" is definitional.

[Anonymous No.9563313]

>>9562242
0,000...01=10^{-n} for some natural n.

[Anonymous No.9563350]

>>9562242
>What does 'infinitesimally small' mean?
It's referencing your penis

[Anonymous No.9563359]

>>9563350
XD rekt

[Anonymous No.9563365]

>>9562256
wrote this incorrectly, I meant to write:

lim (h->0) (f(x) + h) - (f(x)) / h

[Anonymous No.9563571]

>>9562242
It is so small that it can be substituted for 0 without much loss in accuracy.

[Anonymous No.9563593]

>>9562242
by definition in the hyperreals 0.000...;...1 means a number smaller than any other number

people say it doesnt exist becausae theyre a bunch of dumb salty faggots and think 0.999... = 1

[Anonymous No.9563597]

>>9563011
>>9562974
top tier banter

[Anonymous No.9563609]

>>9562242
[math]0.000...1 = lim_{x \to \infty}10^{-x} = 0[/math]