Math problem

[Anonymous No.7491490]

Does 0,999... equal 1?

[Anonymous No.7491494]

If this thread gets any responses, it's proof that /sci/ is entirely newfags, since anyone who's been here more than a week would have seen this thread already and known that it's bait.

[Anonymous No.7491505]

clearly no otherwise they would have written 1, no?

[Anonymous No.7491507]

>>7491494
Let's keep the thread on topic, shall we? Derailing threads is not cool at all friend.

[Anonymous No.7491508]

not 3 fgt

[Anonymous No.7491510]

Yes, write (3 one-thirds = 1) in decimal notation and equate it to the factional form. sz

[Anonymous No.7491511]

>>7491505
We could define some operation and use ? is its sign. You know, like n!, but like n? resulting in n-0.000...0001 with infinitely many zeros in between. But, what is its evolutionary purpose that we could define it like that?

[Anonymous No.7491518]

No it equls .99999999... Dumass

[Anonymous No.7491519]

>>7491511
That's being deliberately dense and pretending you don't understand the concept of positing a mathematical problem as a question.

[Anonymous No.7491524]

>>7491494
This.

[Anonymous No.7491529]

>>7491519
Oh, but I did understand it. I just defined a new operation. But is it well-defined?

Let n and m be integers. If n=m, then n-0.000...0001=m-0.000...0001, so n?=m?, and ? is well-defined. My conjecture is that ? is extendable from the naturals to all reals.

[Anonymous No.7491541]

[Anonymous No.7491550]

>>7491541
but my thread is not stating 0.99... = 1, my thread is questioning if 0.99... = 1
so check-mate friend :^)

[Anonymous No.7491553]

>>7491550
0.99... =/= 1 is what i meant in the first sentence, my mistake

[Anonymous No.7491556]

>>7491529
Incorrect, because you are assuming homogeneous traits over multiple sets, but that does not logically hold.

You did not define a new operation, you created a variable operator that effectively subtracts 1-over-infinity.

[Anonymous No.7491563]

>>7491556
But 0<0.000...0001<1, so I'm not substracting infinity from anything.

[Anonymous No.7491574]

>>7491563
Good for you. Tell your friends you invented a math theorem and did a lot of serious work today.

sage

[Anonymous No.7491596]

>>7491574
You tell me first why you come to these threads looking for intelligent discussion. It is obvious there is no such number as 0.000..0001 with infinitely many zeros, so there is no distinction between 0.999... and 1. And even more importantly, regarding my serious work, I'm having my daily shitposting break. :^)

Just fucking with you, man.

[Anonymous No.7491623]

in the surreals .99... is not equal to 1 right?

.99... plus the infinitesimal e equals 1

[Anonymous No.7491667]

>>7491623
In the surreal numbers, "0.999..." is invalid notation, because the "..." is ill-defined in a system with uncountable zillions of infinities.

You'd have to specify exactly how long of a forever you were summing up 9/(10^n) for. If it's taken to be countable infinity, it'd be 1-epsilon, yes.

[Anonymous No.7491686]

>>7491667
Thank you. I'm just barely into surreals and they're still pretty strange and funky to me.

>If it's taken to be countable infinity, it'd be 1-epsilon, yes

What about an uncountable infinite repeating .99? Would that be something like 1 - e^2 or 1- e^e? Or am I being too ambiguous/misusing repeating decimals to define an uncountable repeating decimal.

[sage in all fields No.7491697]

>>7491490
fuck off
sage in all fields

>>7491541
came to post this
0.9..._=_1_for_faggots_and_retards.jpg

[Anonymous No.7491703]

...999.999... = 0

proof:
...999.999... = ...999 + 0.999...
0.999... = 1

Let x = ...999
then x+1 = ...000 = 0
so x = -1

then ...999 + 0.999... = -1 + 1 = 0
QED

[Anonymous No.7491706]

>>7491686
No; it'd be a different, smaller e. (e1, specifically; countable infinity is omega-zero, first uncountable is omega-1). Uncountable infinity is bigger than countable infinity in the same way that countable infinity is bigger than 1. No amount of mathematical operations on e0 will make it as small as e1.

The chain of increasingly large infinities - omega five, omega ten, omega omega zero, (omega omega omega omega omega.... repeated omega zero times) zero...

The total number of infinites in the surreal numbers is so large that it is too big to be a number. There is no mathematical system in which it is well-defined - because obviously it's too big to fit in the surreals, and the surreals are the largest ordered field.

[Anonymous No.7492119]

>>7491494
You first replied, fucking newfag. You let this happen. GTFO.

[Anonymous No.7493548]

i'm proud of having created this thread
:^)

[Anonymous No.7493583]

<span class="math"> \displaystyle
1 = \frac{3}{3} = 3 \cdot \frac{1}{3} = 3 \cdot 0.\overline{3} = 0.\overline{9}
[/spoiler]

[Anonymous No.7493590]

>>7491490
See
en.wikipedia org/wiki/Geometric_series
en.wikipedia org/wiki/0.999...

[Anonymous No.7493593]

>>7493583
mind = blown

[Prof Sai No.7493615]

>>7491490

It depends on what number system you use. Look up "infinitesimals" and Surreal numbers.

If you respond to this question by locking yourself and the questioner into the Real set, then you are an asshole - that is like insisting that a conversation about fractions take place in Natural numbers.

Also concerning:
> .333... = 1/3 ; 1/3 x 3 = 1

Anyone with a brain ought to look at this "answer" and question the premise that .333... = 1/3. This is just restating the question and passing it off as an "answer"

[Anonymous No.7493633]

>>7493615
So to put it in simplistic words: it's not the same as 1 but it's so close to being 1 that it might aswell be 1?

[Anonymous No.7493645]

Come on, people. Anyone who's taken calculus knows that there's an infinitesimal between 0.99... and 1. That's what the concept of a limit is all about.

[ ] Not Told
[X] Told

[Anonymous No.7493650]

>>7493645
so this? >>7493633

[Anonymous No.7493652]

>>7493650
No I mean in the reals as well.

[None !kJfMul3E7I No.7493681]

what are the janitors doing

[Anonymous No.7493692]

>>7493615
>question the premise that .333... = 1/3
Just when you thought it can't get any dumber, it does.

[Anonymous No.7493703]

>>7491490
STOP.
IT'S FUCKING 1.
THIS SHIT COMES UP ON /SCI/ EVERY FUCKING DAY.
IT'S NOT A FUCKING "MATH PROBLEM".
IT'S A PRINCIPLE OF MATHEMATICS.
2/9 = .22222...
3/9 = .33333...
4/9 = .44444...
...
8/9 = .88888...
9/9 = .99999...

>>7493633
No, it is one. it's not "close" to one. It's not so close that it "might as well be 1". It is another way of representing the same number. Just like you wouldn't say 5/5 is close to 1, 0.999... isn't "close" to 1, it is 1.

In fact, all numbers have an equivalent number which can be found by taking the last place value, subtracting 1, and putting repeating 9s behind it. For example:

14392.2394832 = 14392.2394831999999999...

/saged

[Anonymous No.7493709]

1/3 = 1/3 + (1 - 0.999...) / 3

(1 - 0.999...) / 3 = 0

1 - 0.999... = 0

1 = 0.999...

[Anonymous No.7493713]

>>7493692
1/3 actually equals 0.333... + (1 - 0.999...) / 3

[Anonymous No.7493715]

>>7493703
Calm down! We've already established that there's a difference between "infinitesimally close to 1" and "1", sperglord.

[Prof Sai No.7493745]

>>7493633
>>7493650
>>7493652

The term "Real numbers" is very unfortunate. No one in the "real world" uses real numbers for anything practical.

If you are cutting lumber or weighing a liquid it is fine to assume that .999999 (note: no "...") is equal to 1. Computers use two kinds of numbers, both subsets of the rationals.

If you want to move beyond such constraints, the Real set allows some other objects, but excludes others. There are practical reasons for this, but no reasons that originate within math itself. Why stop with the Reals? Infinity, Sqt(-1), and matrixes aren't in the real set, but are all important and widely recognized.

And so are infinitesimals. If someone is asking about a number that is somehow infinitely close to 1, but isn't quite equal to it - well that is a good description of an infinitesimal! Infinitesimals have a wikipedia page, but some people treat it like some kind of forbidden knowledge. Maybe people who DIDN'T spot the circular logic of ".333... x 3" are afraid of what else other people might discover.

[Anonymous No.7493746]

>>7493713
1/3 actually equals
<span class="math"> \displaystyle
= 0.1_{3}[/spoiler]

[Anonymous No.7493754]

>>7493583
How does one prove that 1/3 = 0.3333...? I am dumbo

[Prof Sai No.7493756]

>>7493703
>STOP.
>IT'S FUCKING 1.
>THIS SHIT COMES UP ON /SCI/ EVERY FUCKING DAY.

Why do you think this keeps coming up? Isn't it possible that you, not everyone else, are the one who isn't seeing something?

>IT'S A PRINCIPLE OF MATHEMATICS.
>2/9 = .22222...
>3/9 = .33333...
>4/9 = .44444...

You make it sound more like a prayer then a principal.

[Anonymous No.7493823]

>>7493754
do the division by hand - feel free to show us where the algorithm stops spitting out threes

[Anonymous No.7493829]

>>7493681
>he doesn't love 0.999... threads
u gay ???

[Anonymous No.7493848]

>>7493823
>do division by hand

[Anonymous No.7493854]

For anyone genuinely curious, yes they are equal.

Why is 1/2 = 2/4? They look different, so surely they must be! Nope, we define two rational numbers a/b, c/d to be equal when ad - bc = 0, so every pair of integers does not give a different rational number, i.e. (1,2) and (2,4) are the same rational number despite being different pairs of integers.

Similarly, we define real numbers to be equal under certain circumstances. By the construction of the real numbers, each one can be approximated by rational numbers. If a_n is a sequence of rational numbers converging to a, then we say to real numbers a and b are equal if and only if the limit of a_n - b_n goes to 0 in the rationals.

Now we let <div class="math">a_n = \sum_{i=1}^n 9 (1/10)^i.</div>

By definition of notation, 0.999... = <span class="math">\lim_{n \to \infty} a_n[/spoiler]. But we can write <span class="math">a_n[/spoiler] in closed form as <span class="math">a_n = 9\frac{1-(1/10)^{i+1}}{1-1/10} - 9[/spoiler] using geometric sums which has limit equal to 1. Hence <span class="math">1-a_n[/spoiler] tends to zero, so <span class="math">\lim a_n = 0.999... = 1.[/spoiler]

[Anonymous No.7493858]

>>7493848
and now do it with 1/3