/jp/ - Otaku Culture

inb4 trolls and morons

No, the ... means there's an infinitely small bit that it's smaller than 1.

Sup, /b/ of old.

http://en.wikipedia.org/wiki/0.9
Discussion over.

>>3565142
so much bullshit in that article. 0.9... can never reach one

No

>>3565146
You have a faulty concept of infinity. 0.99 to infinity DOES equal one. You're just repeating 0.9 + 0.09 etc etc in your head and saying it doesn't equal one (true), but the concept of INFINITY does not work that way.

>>3565127
Yes.

inb4 193 posts and 15 image replies omitted. Click Reply to view.

>>3565146
>so much bullshit in that article.
Translated: I CAN'T READ PROOFS! >:(

>>3565161
Frankly I find the proofs to be crap. I really do think its a bunch of supposedly smart people making shit up to try and make themselves sound smarter than they are.

>>3565155
So at what point in infinity does it suddenly go from just short of 1, to exactly 1?

PEOPLE

RESIST THE URGE TO WIN AN ARGUMENT ON THE INTERNET

DON'T POST IN THIS THREAD, YOU'LL GET NOWHERE

>>3565165

THIS. Thank you, Anon!

Stupid smart people!

Think of it this way...

1 - 0.999... = 0.000...01

Since it takes infinite zeroes to reach the one. the answer is, indeed, just zero.
Understanding this takes some knowledge of the concept of infinite. Refer to the infinite monkey theorem if you want to learn more. http://en.wikipedia.org/wiki/Infinite_monkey_theorem

Wait, when did "infinitely approaches" become "equals," huh? Did I miss the memo?

>>3565169
>So at what point in infinity
>using the word "point" in reference to infinity
Allow me to restate that part about your concept of infinity being fucked.

>>3565165
>Frankly I find the proofs to be crap
Translation: I only read the first one and I couldn't understand it.

>>3565171
You shut your mouth, even this retarded troll-bait is better than the rest of the dog vomit all over /jp/ constantly.

>>3565177
No, 1 - 0.9999... = 0

1 - 0.9999...9 would be 0.000...1.

0.9999... = 1
0.999...9 != 1

>>3565185
>So at what point in infinity
>using the word "point" in reference to infinity
>Allow me to restate that part about your concept of infinity being fucked.

You assume that the term point wasn't being used with the same context you are thinking

yeah it equals one it's close enough to one that you can use the value in real world calculations with accuracy.

Hey guys, I heard that you like math, so...

Find the value of x.
It CAN be determined, and there's only ONE valid value of x. If you get to a point where "x can be anything", you did it wrong.

>>3565221
YOU BASTARD!

>>3565209
It's not close enough to one. It IS one. It's the same number, just a different way to write it. It's the number "1" to the same degree that "1", "2/2" or "1.0000..." are.

This stupid thread again?

hey guys.

math is actually arbitrary.

0.999... equals whatever you want it to.

>>3565133
They don't do math on /b/. Also, I kind of like these threads. If you can ignore the Cirno, these threads always manage to spark constructive debates.

>>3565221
I'm tapped out

Hey guys, the set R (of real numbers) and Z (of integers) are both infinite.

Does R have more elements than Z? Discuss

>>3565265


Damn, bro, you suck

>>3565270
>>3565270

R has more. R contains Z as well as every fraction/decimal between every integer.

All numbers are all numbers

>>3565265

remember what you learned about opposite angles, bro.

>>3565221
50 degrees?

A bus left the Scarlet Devil Mansion and three people boarded there. At Hakugyokuroo, one person left and half a person boarded. At Yakumo's house, two people left. How many people are there on the bus?

If you think that
>0.9 + 0.09 + 0.009 + 0.0009 + ... < 1
because the series will only reach an infinitesimally smaller number than 1, then you would also think that
>1/2 + 1/4 + 1/8 + 1/16 + ... < 1
which is Zeno's paradox that proves motion can't exist.

So, if you can move your hands the distance to the keyboard to reply to this (after moving half the distance to the keyboard, then half the remaining distance, and so on to infinity) you've proved yourself wrong.

>>3565293
Shouldn't the top angle be 20 degrees?

>>3565321
There are no buses in Gensokyo.

>>3565343

>>3565321

I don't fucking know. Why the fuck should I know? Ask Yakumo.

>>3565253
Different guy here, but during the brief time I used to lurk /b/ ~3 years ago, I did see this thread on there, and it had quite a lot of activity.

>these threads always manage to spark constructive debates
No, they don't. There's a fairly rigid correct answer, so most arguments against are simply flawed or emotional.

spoiling the fun


gnight amz

>>3565374
>No, they don't. There's a fairly rigid correct answer, so most arguments against are simply flawed or emotional.

yea those idiots who think it equals 1 are rather pissy

I can't get any further without either drawing it to scale and measuring, or using trig. I'm assuming it can be done without either? What am I missing here?

        x = 0.999...
     10x = 9.999...
10x - x = 9.999... - 0.999...
       9x = 9
         x = 1

>>3565382
This is considered middle-school homework level difficulty in my country.

Alright, I think the trick is to set up a system of equations. However, I can't get enough equations to find a solution yet. This is what I have so far:

w + x = 110
w + y = 130
y + z = 160
x + z = 140

I think I need a w + z equation to solve this, but I can't find a relationship between them. The equation must be derived from the triangle, not the preexisting equations to work. If I can get that, I can just use my calculator to get the solution.

>>3565382
Nooooooo.
I was about to solve it

>>3565382
What is this sorcery? God fucking damn it, I hate geometrical properties.

>>3565221
30 degrees, right?

lol for adults you guys sure have a lot of difficulty solving this problem.

>>3565408
Trying too hard. The sum of any angles in a triangle is 180.. so just add and subtract.

>>3565411
Most of /jp/ haven't been to school for many years and are out of shape for doing math.

>>3565411
Most adults are shit at math if you haven't noticed.

God, not this discussion again. The mathfag in me rages at the idiots who don't get it.

>>3565428
>>3565411
No. They are idiots from /g/ and other boards who think that shitposting==trolling. Don't talk to them, don't talk about them.

>>3565417
>from doing meth
is how I read that last part.

I should stop thinking about Breaking Bad.

>>3565411

People just forget stuff they don't use often. Not everyone here is a major in some field that requires math.

>>3565382
Wait, wait, wait. How do you prove that BD = BC = BF? Isosceles triangles only need to have the same lengths for two sides and the only guarantee of two unscaled isosceles triangles with the same angles is that they have the same length ratios.

>>3565417
This is a lie, most /jp/ers MIT students studying SICP.

There is no number between 0.999... and 1 so they are the same number.

>>3565417
This. I haven't done anything related to geometry since I took the SATs way back in high school.

>>3565441
shitty coursebook is shitty

>>3565416
It's not that simple. If you only attempt to solve it with A+B+C=180 there are multiple possibilities, but there is only one true answer.

>>3565439
Basically all the isosceles triangles have one of their two equal sides in common with another isosceles's two equal sides, which allows you to determine which sides are equal. To be more specific, you can immediately find that BD = BC because the angles are 50-50-80. Then you find that BC = BF because the angles of THAT triangle are 80-80-20.

>>3565439
Isosceles triangles also have two identical angles, each opposite to one of the two equal-sized side. This property goes both ways, so any triangle that has two equal angles is isosceles, and the equal sides are the two opposite to the two equal angles.

>>3565466 here
To be honest, I don't know how anyone could actually figure that out without seeing the answer beforehand. How does one know where to draw the imaginary lines, and at what angle? That's the real tricky part of the solution, I think.

>>3565463
How dare you insult the holy SICP? :(

I think I did it right....

In relation to the original problem...

If my finger STARTS exactly one inch from the keyboard, and I move it 0.999... inches, will it ever touch the keyboard?

Assume both surfaces are perfectly flat and never change.

Also see http://en.wikipedia.org/wiki/Zeno%27s_paradox#The_dichotomy_paradox

>>3565466
>>3565467
I see it now. Thanks for clearing it up.

>>3565482
Define "touch".

>>3565482
go back to where you came from.

>>3565482
So you start one inch away from keyboard and move one inch? Sure, it'll touch.

>>3565475
>How does one know where to draw the imaginary lines, and at what angle?
You draw them at angles that create isoceles triangles, so that each line you draw is the same length as an existing line.

>>3565488
as in makes contact, wtf else would I mean?

>>3565478
How did you come to that angles CDE and EDB equal 50 and 80, respectively?

simpler proof;

0.3 + 0.3 + 0.3 = 0.9
0.333... + 0.333... + 0.333... = 0.999...
1/3 = 0.333...
1/3 + 1/3 + 1/3 = 1

SO MANY FUCKING RETARDS IN THIS THREAD.

0.9999... = 1.

IF YOU DON'T AGREE, YOU HAVEN'T TAKEN CALCULUS AND ARE A FUCKTARDED FAGGOT.

>>3565500
I just assumed ABC was a triangle and that ADC was a straight line. If it's not, then I'm wrong.

>>3565482
If my balls start exactly one inch from your balls, and I move them 0.999... inches towards yours, is it gay?

>>3565513
You can stay right where you are faggot

>>3565510
Actually if you'd learned anything you'd know that it can be either depending on the context and your purposes.

>>3565512
That only tells you that CDE and EDB combined equals 130, not their individual values.

>>3565510
All caps and swearing doesn't make the theory (And if you're going to be pedantic, unproven theory) true.

Also, Occams razor.
0.999... not equalling 1 is a lot simpler than anything else.

>>3565510
Nice try bro. 0.999 repeating is not the same as 1. It's simply infinitely close to being 1 that some say they're the same.

hey guys, if 0.999... is not 1, then how much is 1 - 0.999...?

Sauce for bakas:
#1 http://en.wikipedia.org/wiki/0.999......
#2 Cirno's Perfect Math Class
#3 Common Sense & Logic 101

>>3565527
Ah, shit, you're right... And here I was thinking I was smart or something....

>>3565482
The fact that your finger is "flat" is much more concerning than whether or not it is touching the keyboard. You should see a doctor about that.

Also, you forgot to factor Heisenberg Uncertainty into that question.

>>3565536
1 - 0,999... = 0 because both numbers represent the same real number.

>>3565528
Occam's razor doesn't apply because you make different conclusions. It would only apply if both of you said .999... equaled 1.

>>3565536
3

>>3565543
Yes, but I wonder what do the 1 != 0.999... people think about it. Assuming that they "think".

>>3565538
I'm going to be a jerk because this discussion needs more posts. Do you have a proof for:

0.999(inf) + 0.999(inf) = 1.999(inf)

>>3565543
Only if you're not using a branch of mathematics that stipulates the existence of infinitesimals.

>>3565538
you lost me

>>3565549
Yes.
0.999... = 1
1.999... = 2
1 + 1 = 2 [citation needed]
Therefore,
0.999... + 0.999... = 1.999...

>>3565528
>>3565523

No you have absolutely no understanding of infinity if you cannot understand that 0.999...= 1.

There is no debate on this issue. It is as simple as saying 0.3333... = 1/3. It doesn't "approach" three, it fucking equals three.

Also, I'm a fucking cs major and yes I'm going to swear because I don't have patience for this bullshit. It depresses me that people can call themselves adults and cannot even understand something as fundamental as rational numbers. To put it simply, 0.99999... is the decimal expansion of 1 in the same way that 0.66666... is the decimal expansion of 2/3. They are two different ways of saying the same exact thing. There are numerous proofs of this and the fact that you would be so arrogant as to dismiss said proofs means it's pointless arguing with you.

I got lost on like the tenth fucking post in this thread

And to think, I used to want to be a physicist.
Fucking hell, this is what makes NEETs withdraw from society

>>3565562
It completely depends on the context it's being used you retard. 1/3=0.333... simply because we have no better way of expressing it. 1 > 0.999...

>>3565570
On what context is bloody 0.333... not the same as 1/3?

>>3565571
I said it is = to 1/3 learn to read bro.

>>3565571
You should go to college. You learn many nice things there.

>>3565576
>>3565571

Unfortunately, you must go to a community college if you honestly believe that 0.9999... doesn't equal 1.

>>3565568
If you have the passion for physics, then go for it. Just find a good teacher for yourself unlike the goons in this thread.

>>3565581
Nice response bro, don't add anything.

induring obvious KoG metathread

>>3565562
I don't like the way this works out x = .999999... y = 1
x ￥ y = 0
|x| - |y| = 0
√xy = 1
x^y = 1

>>3565581
>does not grasp the meaning of infinty
>puts the word "belief" into maths
>ignores infinte proofs that 0,99.. = 1
gtfo

>>3565587

/jp/ is really losing its mind if it took this long.

Either that or I'm getting better at samefagging.

>>3565591
What the hell does the yen sign mean?

>>3565595

>5

>>3565591

I don't understand why people freak out about the fact that 0.9999... = 1. If you really want some mind-blowing shit, check out Euler's identity (see pic).

Once again, there are literally hundreds of proofs for this and it's not exactly like this is a new theorem (it's been around since the 18th century).

>>3565598
'/' I assume.

>>3565598

Yen sign is probably referring to the modulus operator (designated by the % in western programming). The modulus operator divides the two terms and displays the remainder. Since 0.999... = 1, there is no remainder, thus it is equal to 0.

>>3565607
It's a combination of idiots and trolls--welcome to 4chan. And as a mathfag myself, Euler's identity is some pretty sexy stuff, or more generally, e^(xi) = cos x + i sin x.

>>3565615
Neat. I'm a bio major and this thread has been very informative.

>>3565615
Actually, % usually means the REMAINDER operation, which is similar but not identical to the modulus operation (the difference has to do with signs when dealing with negative numbers).

So what you mathfags are saying is, even though it is PHYSICALLY impossible for you to ever reach a point 0.999... away if you start at the 1 mark, you CAN reach it mathematically? This is where I usually would scream at my math teacher and tell her this shit has no meaning in real life.

>>3565640

Asymptotes actually do have meaning in real life...
They're pretty much the bread and butter of economics.

>>3565607
The result of an exponentiation can never be negative and whoever 'invented' i and the complex numbers should have been burned at the stake for this. Fucking witchcraft.

>>3565644
I'm going to harm you now

>>3565652
Hey, complex numbers are useful in geometry, and their 3D version, Quaternions, are made of <3 if you're working with 3D stuff (notably, 3D graphics).

>>3565637

I have no idea what you're talking about. Almost every single computer class I've taken have said they're one and the same thing. You could make an argument that the remainder operator is different in that certain languages reverse the order of the operation by making two different operators, namely REMAINDER and % but in most high level languages, there is no need. Look at Java and C++ (or C#) for example, both languages don't even have a REMAINDER operator.

>>3565637

I have no idea what you're talking about. Almost every single computer class I've taken have said they're one and the same thing. I suppose older languages use two different operators, namely mod and rem, but that was probably due to the fact that older computers would error out if they tried to perform that operation with a zero denominator. Look at Java and C++ (or C#) for example, both languages don't even have a REMAINDER operator; they only use the %. See Wikipedia for more details:

http://en.wikipedia.org/wiki/Modulo_operation

>>3565701
Older? More like GOOD languages offer both, while those designed for hacks or speed only offer one (note how Haskell, ML and Prolog, very mathy languages, offer both). But I suppose that neither is more or less "correct". It's just sad that C and derivatives mostly take the road of "take sign of dividend", which is almost always more annoying than taking sign of divisor.

So, is 0.⑨⑨⑨⑨⑨⑨⑨⑨... = 1 baka?

>>3565742

>>3565732
how do you define a good language anyways? languages come and go every couple of years/decade, yet here we are, still using C++ from...what is it, the 70s? not to mention assembly.

>>3565779
And Lisp, from 1959. Which is, incidentally, arguably better than most languages of today.

Almost FV quality thread ;_;
These threads keep reminding me how a lot of people fail at math.
Also, troll thread, I should report it.

On-topic reply:
>>3565615
>Yen sign is probably referring to the modulus operator (designated by the % in western programming). The modulus operator divides the two terms and displays the remainder. Since 0.999... = 1, there is no remainder, thus it is equal to 0.

Modulo arithmetic only works in Z, while getting the floor/ceiling of a Real/Rational number is a different operation. Some programming languages might implement both through the same operator/function, but they're different things. I suggest you do not mix practical programming with real maths. Operations in popular programming languages tend to be designed to be executed efficiently on some platform thus they only work with some specific number types(which do have proper formal representation in math), but they're different from +/-* over N,Z,Q,R,C. Some languages do this much better, others have libraries which allow arbitrary precision calculations, but doing any(however, many are possible) operation over R,C is pretty much impossible on a computer, as you'd need infinite resources/time. Of course, you can do some symbolic reasoning and operations using a theorem prover or more specialized languages, but those are different things, but when people refer to the default arithmetic ops available in C,C++,Java,C# and think they represent the math they were thought in school...

>>3565783
wait, does lisp support object orientation (right now)?

>>3565732

I'm trying to understand this. So basically, the only difference between mod and rem is how the program treats the sign of the final result? In one, it takes the sign of the divisor and applies it to the final result while in the other it uses the sign of the dividend, correct?

I guess that makes sense since if you were to try and create a boolean test trying to determine if a given number is odd, then using the wrong operator could result in a fake false result when a function is actually supposed to be true due to the fact that it made the function return a negative, which the test wasn't designed to handle.

Am I understanding this correctly?

　　　　　　　.i＼ ／i
　　　　　　＜ '´ ￣　ヽ
　　　　　＿_彡ﾉﾒﾉﾉlﾉﾘ〉
　　　 　.＼ ｀ｿﾘ!ﾟ ヮﾟﾉi　　0.999... != 1
　　　　　　 ＞<(つ!>つ　　
　　　　　 /　,く//_|l〉　
　　　　　 ￣　l.ﾉl.ﾉ 　　

>>3565790
Lisp is functional, which is a type of declarative programming. Object-Orientation is a derivation of structured programming, which is a type of imperative programming. One is based on Lambda calculus; the other on Turing machines. Apples and Oranges. Some languages try to support both (e.g. O'Caml, Python), but usually sacrifice functional purity for that.

>>3565732
Haskell does it well. I also like how Lisp does it: proper bignum support, automatic upgrading from fixnum to bignum, rations, arbitrary precision is easy to implement(albeit can be slow if done incorrectly). Another cool thing is that FLOOR, CEILING, TRUNCATE, ROUND return multiple values (both quotient and remainder), which is actually both smarter and more efficient: on the x86, if you divide two fixnums(imm32), the quotient is stored in register EAX, while remainder is stored in EDX, which means that when someone does a%b or a/b in C, they discard one of the values, even when they need both. Some smart C compilers can actually optimize this, but it's stupid nonetheless.

>>3565787

So how would you do a modulo operation using rational numbers (which would apply when trying to do 0.9999... % 1)? I'm curious since it's not actually possible to write the decimal expansion of 1 into a computer program but if we were to test divisibility of, say, 0.5 into 1, what would the operator be?

>>3565797
Well, it's no surprise that Cirno would be in the 0.999... != 1 crowd.

>>3565790
Yes, CLOS is better than most `Object-oriented' languages which are popular nowadays. Hell yea generic methods/multimethods and properly separating data structures from functions and allowing specializing generic functions on them. Also, amazing MOP.
P.S.: I'm glad to see there's other Lispers on /jp/

>>3565817
　　　　　　　.i＼ ／i
　　　　　　＜ '´ ￣　ヽ
　　　　　＿_彡ﾉﾒﾉﾉlﾉﾘ〉
　　　 　.＼ ｀ｿﾘ!ﾟ ヮﾟﾉi　　HOORAY!
　　　　　　 ＞<(つ!>つ　　
　　　　　 /　,く//_|l〉　
　　　　　 ￣　l.ﾉl.ﾉ 　　

ITT:
- Math
- Touhou
- Programming

<3 4chan

I've completed 900+ pages of Stewart's Calculus book making me superior to all of you. ^_^

And on top of that I'm the proprietor of /bun/. Just face it, you'll never be half as good as me.

>>3565984
>>3565984,1
Such a wit we have here.

mathematically 0.99~~~ will never be equal to 1.0 but since the difference of 1.0's value and 0.99~~ is so small that its considered insignificant, meaning using 0.99~~~ and 1.0 wont matter if used in a mathematical equation.

Cirno is still a baka lol

>>3566039
3/3 = 1

God damn it why is this so hard.

Requesting threadban.