/sci/ - Science & Math

>>12088692
>t. pleb who can't grasp and understand what infinity is

>>12088702
green text and slamming your hand to fill up the response with nonsensical letters is not an argument
explain how to reach 2 or have sex

who said a sequence must attain its limit in the euclidean metric?

>>12088709
>have sex
bait and shitpost more

0.999... never reaches 1.

But the limit of 0.999 is 1.

>>12088714
how can there be a limit to hit when you can just keep adding 9s to 0.999 forever?

>>12088692
Wow OP Ive never actually though of that. This is definitely the first time I'm seeing this thread on /sci/. I really think you might be a genius OP. How could mathematicians have never thought about that? It's insane.
Are your parents academics by any chance?

>>12088736
It's scary to think that geniuses like OP are posting in such a lowly website. Makes you think who else lurks here?

>>12088692
Amazing. You're like a Mozart of maths.

>>12088736
I never implied I came up with it first, just wanted to see if someone here could come up with a justification for pretending that we could ever reach a full number, but I suppose not.
I was hoping it could make it sense, but all I get is anger over what is looking like a made up social construct.

>>12088754
We're all marvelling at your ingenuity.

>>12088736
>>12088774
cringe

Two numbers [a,b] are different if there exists at least one third number [c] between them that is not [a] or [b].
Between 1.999... with an infinite amount of nines and 2 is 1.999... with an infinite amount of nines because if you add another nine you've still got 1.999... with an infinite amount of nines.
Therefore they fail the test in the first sentence and are not different numbers.

>>12088692
[math]1.999\dots = \sup\{ 1.9,1.99,1.999,\dots \}[/math] i.e. the smallest number which is [math]\geq[/math] than 1.9, than 1.99, than 1.999 etc. it can be proved that there can be at most one number with this property and that 2 satisfies this property. therefore 2 and 1.999... denotes the same number.

>>12088719
because you don't know what limit means

Let epsilon = 1 - 0.999...

>>12090510
so, epsilon = 0

>>12088979
Limit, mathematical concept based on the idea of closeness, is used primarily to assign values to certain functions at points where no values are defined, in such a way as to be consistent with nearby values.

everyone who doesn't know this is a pajeet who claims that the undefined value of a theoretical limit is actually defined.

0.999... is not a strictly defined number, there's no infinitesimals in reals, but learning hyperreals and defining an infinitely small difference between 0.999... and 1 is insanely hard for pajeets and 0.999... = 1 is easy so that's what they do.

Geometric sums are retarded and misused to claim otherwise, and it is inconsistent with itself, because geometric sums depend on limits, they abuse the fact that a limit is just the "actual value".

0.999... can be defined as

[eqn]9\cdot10^{x}+10^{-x}=1[/eqn]

none of you niggers can find a real positive number that doesn't fit in, proving that you brainlets can't cope with reality and take shortcuts just to pretend that you're smart.

>>12090566
and if you were about to nitpick that I forgot -x, kill yourself.

Updated:

[eqn]\frac{9}{10^x}+\frac{1}{10^x}=1[/eqn]

>>12088714
0.999... is static, the length is aleph_0 from the get go.
Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.

>another 0.999 != 1 thread
LATEX TEST

$\sum_A^B$
$\prod_A^B$
$\int_A^B$
$\left( \frac{\int_a^bxdx}{2} \right)$

forgive me faggots

>>12090566
[math] \displaystyle
0. \bar{0}1
= \lim_{n \to \infty} 0. \underbrace{0 \dots 0}_{n ~ \text{times}}1
= \lim_{n \to \infty}
\left [
\left (
\sum_{k=1}^n \dfrac{0}{10^k}
\right )
+ \dfrac{1}{10^{n+1}}
\right ]
=0
[/math]

>>12090690
Oh I get it
LATEX TEST 2

[math]
$\sum_A^B$
$\prod_A^B$
$\int_A^B$
$\left( \frac{\int_a^bxdx}{2} \right)$
[/math]

>>12090697
Oh Oh the $'s are unneeded it seems
LATEX TEST 3

[math]
\sum_A^B

\prod_A^B

\int_A^B

\left( \frac{\int_a^bxdx}{2} \right)

[/math]

>>12090699
last one
[math]
\sum_A^B \\
\prod_A^B \\
\int_A^B \\
\left( \frac{\int_a^bxdx}{2} \right)
[/math]

>>12090696
That's the limit.


Now the value? What's the x? Give me a real number for x above so that [math]\frac{1}{10^x}[/math] truly becomes 0.

If you can't tell me, I'm not even going to humor other retarded "proofs" that contradict the fact that neither part reaches 1 or 0 respectively.

>>12090702
yes it worked
good
thanks for your patience

>>12090702
LaTeX was made by humans and you could make it evaluate that 1 = 2 you retard, its not omnipotent source of knowledge.

>>12090705
let's hear your definition of 0.999...

>>12090713
dude, I'm literally using your shitty thread to test if my latex code works with random numbers

>>12090705
>real number for x
sigh. it says x --> inf
1/inf=0

>>12090716
Its undefined, you cannot grok it mainly because your IQ is too low to comprehend infinitesimals and therefore they "don't exist".

>>12090721
>Its undefined
topkek

>>12090720
infinity is not a real number or even a number.

I say real as in a number from real number set you nigger.

>>12090721
>Its undefined
how come real analysis textbooks (and also wikipedia for example) think it's defined perfectly well?

>>12090728
lrn2math
if it says x--> inf then that's what happens
your autism doesn't change it

>>12090727
if you find this funny I assume you're one of these cs inbreds who thinks that 1/0 = inf just because IEEE 754 defined it that way due to its usefulness and your shitbrain assumed that that's how math works.

>>12090729
>muh authority
before you come up with a real argument, lets talk about why so many people believe in god and how majority means the ultimate truth.

>>12090721
Can't help taking the bait, but do you know most rational numbers don't have a finite decimal representation? Does it mean that they don't exist as well?

>>12090737
you haven't answered my question. are you saying 99% of mathematicians are simply wrong?

>>12090734
>just because IEEE 754 defined it
and any uni math course, anyone serious with math
only 4chan schizos twitch endlessly over it
[math] \displaystyle
\lim_{x \to \infty} \dfrac{x+1}{x} =
\lim_{x \to \infty} 1+ 1/x = 1+0 = 1
[/math]

>>12090743
99% mathematicians most likely don't have enough free time to argue about whether infinitely small gaps do exist between numbers or not, simply let it go and never thought about it again because its mostly irrelevant to them whether its 1-0.0...1 or just 1. They will use limits and pretend that its okay. When limits in the first place are used to talk about values in function ranges that are UNDEFINED.

Also infinitesimals and hyperreals are for some reason ignored completely instead of used together with limits and this inbred laziness is exactly what spawns these kinds of arguments.


TL;DR yes.

>>12090747
Limits are specifically for talking about undefined values and hypothetical, uh, limits.

When in context of limits, 1/0 actually means divergence, nothing else, it still is not defined as any real number you nigger. Infinity is not a number.

>>12090760
>Infinity is not a number.
so what

1/inf = 0
1 + inf = inf
1- inf = -inf
inf + inf = inf
inf/inf undefined
inf-inf undefined
1^inf undefined

you can't do everything with inf as with a number, doesn't mean you can do nothing tho

>>12090753
well, 99% mathematicians agree that [math]0.999\dots[/math] is defined as [math]\lim_{n\to\infty}\sum_{k=1}^n \frac{9}{10^k}[/math]. so your claim that it's undefined is objectively wrong.

>>12090767
Only in context of limits you inbred.

>>12090772
Yes, a limit. it is defined as a LIMIT because Real value literally is undefined.

If you were a real mathematician, you could at least figure out the difference without me spelling it out for you.

>>12090777
a limit (if it exists) is a real number, anon

>>12090773
>Only in context of limits
only if you stay within R
Include a separate -inf to the left and a separate inf to the right of R

>>12090783
Limit is not value.

[eqn]lim_{x \to \infty}\frac{1}{x}=\frac{1}{\infty}=0[/eqn]

Yes, limit is 0, but its literally never 0, no real number will satisfy [math]\frac{1}{x}=0[/math] that's like... exactly why we use limits you shitbrain, to define hypothetical limits of values that otherwise are undefined.

Same with 0.999... we can define its limit, but its value with our current math is undefined.

Only shitbrain self proclaimed mathematicians will define value of 0.999... as 1.

You aren't engineers, you can't just round to whole and act like its exact/good enough value, retards.

>>12090796
0.999... doesn't have a limit, anon. it's a real number, which is defined as a limit of certain sequence/function. it's not the function itself.
[math]0.999\dots = \lim_{n \to\infty}\sum_{k=1}^n\frac{9}{10^k} = 1[/math]. you've already acknowledged that the first equality is the generally accepted definition of 0.999..., so do you now claim that the second equality doesn't hold?

>>12088692
No, there is infinite decimation/representation between any integers.

>>12090810
Yeah it doesn't have a limit, it is a limit itself, i know that you shitbrain.

>>12090814
so [math]\lim_{n \to \infty} \sum_{k=1}^n \frac{9}{10^k} = 1[/math] is what you disagree with?

>>12090820
No, I disagree that a value of a limit of a function is same as actual value at that function, because its not. It doesn't help that the position that could be compared to the limit is also undefinable, otherwise, surprise, we wouldn't need limits.

>>12090827
>I disagree that a value of a limit of a function is same as actual value at that function, because its not.
nobody claims that, anon. I'll ask again:
do you disagree with [math]0.999\dots = \lim_{n\to\infty}\sum_{k=1}^n \frac{9}{10^k}[/math]?
do you disagree with [math]\lim_{n\to\infty}\sum_{k=1}^n \frac{9}{10^k}= 1[/math]?

>>12090785
[math]
\stackrel{\stackrel{\bullet}{}} {-\infty}
\stackrel{\frac{~}{~~~~~~~~~~}} {\mathbb{R}}
\stackrel{\stackrel{\bullet}{}} {\infty}
[/math]

>>12090830
no.

>>12090843
so you disagree that if [math]a=b[/math] and [math]b=c[/math], then [math]a=c[/math]?

>>12090847
no.

>>12090852
so you agree that [math]0.999\dots = 1[/math]

>>12090854
no I don't agree with this bullshit statement.

>>12090827
0.999... isn't a value of the function though, it is the limit of the function. The limit has a value, regardless of if that value is within the range of a function.

[math]
1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}
[/math]

>>12090862
assumes that 0.3... = 1/3, not a proof, just extrapolation of 0.999... = 1, if only the latter were true...

>>12090860
you're contradicting yourself, anon. how does [math]0.999\dots = \lim_{n\to\infty}\sum_{n=1}^k \frac{9}{10^k}[/math] and [math]\lim_{n\to\infty}\sum_{n=1}^k \frac{9}{10^k} = 1[/math] not imply [math]0.999\dots = 1[/math]? seems like you haven't thought this through.

>>12090865
>0.3... = 1/3
prove it isn't, and then tell us what it is then

>>12090876
0.3... is 0.3... and 1/3 is 1/3

>>12090876
>prove it isn't
did I fucking stutter

>>12090877
>prove it isn't
did I fucking stutter

>>12090879
Does "." look like a "/" t you?

>>12090860
waiting for your answer to >>12090867

>>12090884
retard
3/5 doesn't look like 0.6... either

Divide 1 by 9. You've got 0.1111...
Now multiply by 9. You've got 0.9999...
The same time, you're back at 1.

>>12088692
1.999... + 0.000...01 = 2
1.999... + 0 = 2
2 + 0.000...01 = 2
2 + 0 = 2

all are true. does that make sense

>>12088907
1.999... is the closest possible number to 2, so of course there isn't another number between them. It doesn't follow from this that they are the same number.

>>12090721
go to bed eric

>>12094182
>closest possible number
no such thing

>>12094198
1.999... is the closest possible real to 2 that is less than 2
1 is the closest possible whole number to 2 that is less than 2

Are you serious or something?

>>12094208
>1 is the closest possible whole number to 2 that is less than 2
true
>1.999... is the closest possible real to 2 that is less than 2
false

>>12088907
>Two numbers [a,b] are different if there exists at least one third number [c] between them that is not [a] or [b].
Turns out that 2 and 3 are not different.

>>12090884
okay now youre obviously baiting.

>>12094220
>Integers are an ordered field.