10 = 9.99999..
x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10
Explain to me why this does not disprove all of mathematics instead of prove that 10 = 9.999999.....?
If a vending machine want's $10 and I put in $9.99 i'm not getting my Pepsi.
Math is a scam.
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Where the fuck did that x - x come from lil brainlet? What you do to the left must also be done to the right. You can't just fucking take stuff out without balancing it out on the other side
Let me reiterate on that, you cannot define 10*9.9999... the same as 99.99999... unless your number terminates or can at least be written as an irrational
>Where the fuck did that x - x come from lil brainlet? What you do to the left must also be done to the right. You can't just fucking take stuff out without balancing it out on the other side
Thats what I thought! This whole thing is bullshit.
>i think inf is a fixed number
samefag
he did do that, you fucking retard.
QUICK RETARD FILTER QUESTION
x + x + x + x + ... (x times) = x^2
differentiate
1 + 1 + 1 + 1 + ... (x times) = 2x
x = 2x
How? If you don't answer why this can't be in 30 seconds your mom will die in her sleep tonight (counter blesses and protections don't work)
>i can use mspaint
sorry, your mom is a retard
but we will always have her pornhub videos to remember her by
Wtf, I don't know
Hope you said bye bye to mommy tonight, brainlets
Shit might be bait, idk, but it's because if given x+x+...+x (n times) = nx, we suppose that n is not a function of x.
But if it is, then we need to apply product rule to n(=x in your case), giving us
(LHS)' = n' * x + n * 1 = 2x = RHS
Sorry for bad formatting, it's 2am here; I'm phoneposting and lazy to latex
>If a vending machine want's $10 and I put in $9.99 i'm not getting my Pepsi.
What kind of pepsi is $10
Why do we have to have this low quality bait every day? Can't we at least get some high quality bait?
it'd be x^x, not x^2.
x+x+x... x times only equals x^2 for integer values of x. The functions aren't identical.
Take a course on Real Analysis, or read a book on it, and specially look at the construction of the Reals.
>tripfag's first real analysis course
You're very special, please teach us senpai.
a = 0.999...
10a = 9.999...
9a = 10a - a = 9
a = 1 = 0.999...
Jesus Christ how stupid can someone be
Don't you guys ever get tired?
Infinity is unachievable. You'll never have anything but a finite amount of numbers in a repeating decimal. If you subtracted some significant amount from a to reduce it to 0.999
a=0.999
10a=9.990
9a = 10a-a = 8.991
a = 8.991÷9 = 0.999
You may then increment a by one more 9 and do the problem again, and continue doing this infinitely, and always get the same answer for a as you started with.
How exactly do you write something as an irrational?
I have been wondering this literally every day of my life
This.
Even if you have an infinite amount of 9's from 0.999... (which you can't, but w/e), multiplying it by 10 reduces the amount of 9's after the decimal. Subtract 0.999... and you're back to having an infinite amount of digits in the decimal where the last value within the infinite, not after the infinite, is 1.
[math]8.\underbrace{999 \cdots 1}_{\infty \text{ digits}}[/math]
you need to put in 9.(9)$
10 dollars
=
9 dollars,
9 dimes,
9 pennies,
9 shinnes,
9 dongols,
9 dennies,
9 zennys,
9 hinnys,
and
9 niggys
You're shortchanging me a niggy.
definition =/= construction
Construct the number 10
0 = {}
1 = {0} U 0
2 = {1] U 1
3 = {2} U 2
4 = {3} U 3
5 = {4} U 4
....
10 = {9} U 9
>÷
fucking reported
I thought I was on /a/ for a second and started to wonder why everyone was acting so retarded. I'm seriously starting to get the impression that Veeky Forums is actually one of the lower-IQ boards on this site.
>I'm seriously starting to get the impression that Veeky Forums is actually one of the lower-IQ boards on this site.
I don't think it is. But it is a board where people learn quickly not to post in any threads that cover their area of expertise, so there is a strong filter where the great majority of posts are by people who have no idea what they are talking about, even if there is quite a lot of actual knowledge present on the board.
Thanks for providing the methodology of being explicitly unable to construct infinity.
>what is transfinite induction
If you draw 0.9, 9, 9, 9 on a numberline and run out of room, you will have drawn a finite number of 9's...
Wikipedia is so retarded omg.
Transfinite oh is that how you cross the missing information gap between finite and infinity?
How is this board so retarded. If 0.(9) has an infinite number of nines after the comma then it must be 1 by definition since it's a real number because it's infinitively close to 1. If it is infinitively close then there can be no numbers in between 0.(9) and 1 which means they are the same number. If it isn't then it wasn't infinite number of nines to begin with.
[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]
There is no such thing as "infinitely close". That is literal gibberish.
The closest anything can be to another thing is a plank length and that is definitely finite.
Seriously you can't even begin to rationally describe what "infinitely close" means.
when will Veeky Forums be able to transcend numberphile tier clickbait?
1/inf=0
protip: same as your iq
its obvious that wiki leaves out detail.
no where did they claim the proof is based on you being physically incapable of drawing more distinct lines
infinitely close is the distance from an open set to a limit point of that open set.
You can actually.
Suppose we have x and y such that y > x. y will be infinitively close if y < a where a is any number that is bigger than x. If y < a is true for any valid a then y is infinitively close to x.
>
>
>You can actually.
>Suppose we have x and y such that y > x. y will be infinitively close if y < a where a is any number that is bigger than x. If y < a is true for any valid a then y is infinitively close to x.
I meant y >= x.
This assumes infinity is a quantity that can be obtained as well as it being a number since it relies on [math]1-x^{\infty}[/math], which means we can just as easily rewrite as [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] where the infinite partial sum is 0 and irrelevant to the sum total meaning all summable work occurred before n=infinity, yet any test of real n doesn't provide an infinite amount of 9's.
Oopsie poopsie!
It actually relies on [math]1-x^{\infty +1}[/math] since [math](1-x)(1 + x + x^2 + x^3) = 1-x^4[/math], so the end of the sequence at [math]\cdots + x^{\infty}[/math] means altogether it's [math]1-x^{\infty +1}[/math], which directly invokes the undefinable vagueness property of accuracy loss by having used infinity when it doesn't even exist, since infinity+1 is not different from infinity by itself. In the end, you actually lose a value.
Rather you gained a value.
ACTUALLY the end of the sequence is [math]\cdots -x^{\infty} + x^{\infty} \big)[/math] and that value is undefined, so you either only get [math]x^{\mathbb{R}}[/math] as a maximum to the sequence or the entire sequence becomes invalidated as undefined. Either way, no longer infinite.
[math]\frac{\mathbb{R}}{\infty} = 0[/math] so thats not saying much. In relation to infinity, 1 is infinitely close to a googol, cause not even 1 with a googolplex googols of zeros after it is anywhere close to infinity.
Great methodology.
In relation to infinity, all numbers have the same value of 0. 1 is no closer to infinity than a billion.
Therefore because infinity, 1 = 1,000,000,000 and also any [math]r \in \mathbb{R} = \text{ any other } r \in \mathbb{R}[/math]
thanks, infinity. Numbers no longer have value and cannot be ordered.
Infinity needs to be redefined as the only number you shouldn't analyze cause doing so would prove it wrong.
Infinity should be redefined as the holocaust.
but then infinity would only have a value of 6 million.
finite doesn't push infinite around
is this surprising to you? baka
>but then infinity would only have a value of 250,000
ftfy
Wtf is wrong with this board. It's supposed to be science and math but it's mathlets everywhere.
>redefined
from what?
A number theory which includes infinity can no longer be well ordered. You want to make sense of the 9's in 0.999... being infinitely close to 1, that doesn't mean much when 1 is then infinitely close to a billion.
>includes infinity
it's kept separate from R
lrn2read
wolframalpha.com
An unbounded quantity that is greater than every real number.
Where the fuck did the post say infinity had to be a real number.
Learn to read retard.
TRY PUTTING $9.99999999... INTO THE VENDING MACHINE IDIOT
∃x( { } ∈ x ∧ ∀u[u ∈ x → ∃y(y ∈ x ∧ u ∈ y ∧ ∀v[v ∈ u → v ∈ y])])
First encountered in axiomatic set theory.
Usually by using this phrase they mean lim Δx→0 [ f(x) = x + Δx ] or similar notion by context.
First encountered in calculus.
>>thread
In the construction of the reals, 1 ≡ seg≤(Q,1). Any set bounded from above at 1 with a proper initial segment and no greatest element is equal to 1 ∈ R by definition. One example of such at set would be A = { 1 - 1/n : n ∈ a+ }.
First encountered in real analysis.
people do it erry day
>A number theory which includes infinity can no longer be well ordered
A NUMBER THEORY that ALLOWS infinity is worthless.
Nothing about the post said real numbers.
You actually need to learn how to read.
>my number theory doesn't include numbers
ok. sounds relaxing.
Construct the triangle of points ABC
A = (0 , 0)
B = (1,000,000,000 , 0)
C= (500,000,000, [math]\sum_{n=1}^{\infty}n[/math])
Our point of view is point C
As C.y goes off to infinity, the lines CA and CB become parallel and overlap. Relative to C, A and B are infinitely close to each other. Therefore 0 = 1,000,000,000
Are we sure we really want to use "infinitely close" to describe a relationshio between 0.999... and 1? Cause it seems like using that methodology, any number can then be equal to any other number.
0.999 repeating is greater than any number less than 1. 1 isn't greater than any number less than 2. So we can very easily see that 1 cannot be infinitively close to 2 but 0.999 can be infinitively close to 1.
Again, you need to read a book on Real Analysis for proper answers.
bro you might be retarded.
Relative to infinity there is zero distance between 1 and a billion. I'm not sure how you failed to understand that, it's directly alloted for by [math]\frac{\mathbb{R}}{\infty} = 0 [/math]. No number rationally exists between 1 and a billion. They are infinitely close to each other.
You might want to ask yourself who's fault it is that you believe so strongly in a fallacy that you will sooner ignore and question the validity of PROOF than change your mind.
Except they aren't because there are infinite number of numbers between 1 and 1 billion just like between 1 billion amd infinity.
Right, but that doesn't matter. There are also an infinite amount of numbers between 0 and 1, but you're not treating them with unique identities there are you?
Your arguement is 0.999... = 1 because there is no positive value to add to 0.999... that will equate 1. The argument in total is that 1 = 1 billion because there is no positive value to add to 1 that will equate 1 billion. Both 1 and 1 billion share the same value identity of 0.
>zero distance between 1 and a billion
can I have my $1 bn now?
As soon as there is infinite money.
Unfortunately infinity doesn't exist.
Even if you did get the money though, it wouldn't actually be worth anything.
No. The argument is that there is no real number between 1 and 0.999 repeating vut there is an infinite reals between 1 and 2.
There exists no number between 1 and 1 billion. They are infinitely close to each other.
Maybe a third time is the charm?
Hello, anybody in there?
> (You)
>There exists no number between 1 and 1 billion. They are infinitely close to each other.
>
>Maybe a third time is the charm?
>Hello, anybody in there?
Okay what. Did you have a stroke there?
Maybe a fourth time will do the trick.
0.999... < r < 1
You believe no number r exists, that the value identity of r must then not be one of a positive number, but instead 0. R itself isn't "0", just that, because you believe there is no r here, the r of the problem has zero relevance.
Now, for 1 < r < 1,000,000,000 ; no r exists here either. There is no positive value r to add to 1, so the valuable identity of r is 0.
1 = 1,000,000,000
there is, infinite far away
Sorry, you're losing the other guy, and me.
There is no Real Number r so that 0.999... < r < 1.
There exists a Real Number r so that 1 < r < 2. For example, 1.5.
Wtf are you talking about
Why would r be 0 here in either case? Who claimed that?
You can't prove 1.5 exists as a number between 1 and 2.
You allow infinity to exist, then all real numbers relative to infinity are infinitely close to each other.
• [math]\frac{\mathbb{R}}{\infty} = 0[/math] means all real numbers have zero value and all real numbers equal each other.
• 1 might be less than 5 relative to 10 since 1 is (10-1):9 away and 5 is (10-5):5 away, but 1 is the same number as 5 relative to infinity since 1 is (inf-1):inf and 5 is (inf-5):inf
f-fifth time is the charm...
>You can't prove 1.5 exists as a number between 1 and 2.
lolwut
>You allow infinity to exist, then all real numbers relative to infinity are infinitely close to each other.
Ok, but I thought we were talking about the Reals, and infinity is not a Real Number. Not sure what you're on about here, but you're completely off-base. No one else is making silly arguments like "well, compared to 1 billion, 0 and 1 are really close". No one is invoking infinity either.
You aren't invoking infinity my claiming 0.999... has an infinite amount of 9's or that it is infinitely close to 1 or that there are infinite numbers between 0 and 1?
Really?
1 is 1 less than 2 no matter if you include infinity or not. Why would you relate anything here to infinity?
2 is just a made up number you invented to pretend there exist values between 1 and 1 billion.
Watch who you call brainlet lol
Not really, no.
Generally in proper mathematical circles, 0.999... (repeating) can be identified in various ways. One can think of it as a decimal expansion. A decimal expansion is a function f : N -> {0, 1, ..., 9}
In this case, the decimal expansion is simply the constant function f(x) = 9
No need for a value of infinity here.
Then, we can use standard calculus limits and the standard construction of the Reals. No infinity values here either.
Infinity isn't a part of real numbers. There is an infinite number of real numbers but that doesn't say that infinity is one of them.
That's like saying that in a set {2, 3} 2 is 1 less than 3 so 1 is involved in the set.
I'm glad you're agreeing there are only a finite amount of 9's in 0.999...
It also works with 0.9999999
I didn't say that. I said that I didn't need the number "infinity". I do need an infinite set, such as Natural Numbers. However, Natural Numbers does not contain the value "infinity".
Guess that means you can't have an infinitr amount of 9's in 0.999... and must therefore only be able to have a finite amount of 9's.