.999... = 1

[Timminz]

If you are 10 feet from the door, and go halfway to the door each time you take a step, how many steps will it take you to get to the door?

1/3 = .3333... = .333333333333333333333 and 1/3 of the digit to the right of that last 3.

The last digit of .333... is 1/3rd of the digit immediately following an infinite number of 3's

There's no such thing as "immediately following" when "infinite" is involved. If it is infinite, there is no end, and thus nothing to be able to follow.

[Snorri1234]

You guys realize that Prowler is a troll, right?

[bedub1]

If you are 10 feet from the door, and go halfway to the door each time you take a step, how many steps will it take you to get to the door?

1/3 = .3333... = .333333333333333333333 and 1/3 of the digit to the right of that last 3.

The last digit of .333... is 1/3rd of the digit immediately following an infinite number of 3's

There's no such thing as "immediately following" when "infinite" is involved. If it is infinite, there is no end, and thus nothing to be able to follow.

yes, I understand, but some people want a "last digit". So if you give them the last digit of "1/3rd" then they are happy.

[Snorri1234]

If you are 10 feet from the door, and go halfway to the door each time you take a step, how many steps will it take you to get to the door?

1/3 = .3333... = .333333333333333333333 and 1/3 of the digit to the right of that last 3.

The last digit of .333... is 1/3rd of the digit immediately following an infinite number of 3's

There's no such thing as "immediately following" when "infinite" is involved. If it is infinite, there is no end, and thus nothing to be able to follow.

lol

[Timminz]

If you are 10 feet from the door, and go halfway to the door each time you take a step, how many steps will it take you to get to the door?

1/3 = .3333... = .333333333333333333333 and 1/3 of the digit to the right of that last 3.

The last digit of .333... is 1/3rd of the digit immediately following an infinite number of 3's

There's no such thing as "immediately following" when "infinite" is involved. If it is infinite, there is no end, and thus nothing to be able to follow.

yes, I understand, but some people want a "last digit". So if you give them the last digit of "1/3rd" then they are happy.

Some people want there to be a god. Just because some people want it, doesn't mean it exists.

[TheProwler]

People will throw equations like this at you:

x = .9999recurring

so

10x = 9.999recurring
-x = 0.9999recurring
---------------------------
9x = 9
x = 1

But don't believe it. Because 9.9999recurring is approaching 10 just a wee bit slower than 0.9999recurring is approaching 1.

if, x=0.999...

then, 10x=9.999...

10x-x = 9
9x = 9
x=1

QED

Think of it as
10x - x = 9.00000...0000001
not 9

It is a deficiency in the way we express a number with an infinite amount of precision. You are off by an infinitely small (but greater than zero) amount.

[Snorri1234]

If you are 10 feet from the door, and go halfway to the door each time you take a step, how many steps will it take you to get to the door?

1/3 = .3333... = .333333333333333333333 and 1/3 of the digit to the right of that last 3.

The last digit of .333... is 1/3rd of the digit immediately following an infinite number of 3's

There's no such thing as "immediately following" when "infinite" is involved. If it is infinite, there is no end, and thus nothing to be able to follow.

yes, I understand, but some people want a "last digit". So if you give them the last digit of "1/3rd" then they are happy.

Some people want there to be a god. Just because some people want it, doesn't mean it exists.

[Timminz]

Think of it as
10x - x = 9.00000...0000001

but it isn't.

0.9999... and 9.9999... have the SAME number of places after the decimal, so each one cancels out the other, when they are subtracted. THERE IS NO REMAINDER.

[bedub1]

If you are 10 feet from the door, and go halfway to the door each time you take a step, how many steps will it take you to get to the door?

1/3 = .3333... = .333333333333333333333 and 1/3 of the digit to the right of that last 3.

The last digit of .333... is 1/3rd of the digit immediately following an infinite number of 3's

There's no such thing as "immediately following" when "infinite" is involved. If it is infinite, there is no end, and thus nothing to be able to follow.

yes, I understand, but some people want a "last digit". So if you give them the last digit of "1/3rd" then they are happy.

Some people want there to be a god. Just because some people want it, doesn't mean it exists.

dude...you are gay. don't touch my wiener.

[TheProwler]

I am quite sure, now that I see how difficult it is for people to get their heads around 0.333recurring and proper the proper use of arithmetic on numbers expressed this way, that this has been the motivation for mathematicians to just announce 0.999recurring equals 1 - to be done with it and start to get some work done. Or, maybe it is just the very top tier that have had to say "Shit, let's drop it. You're never going to understand."

So wait....wait wait...this is actually hilarious. So wait...

You claim that 0.9999 recurring was made 1 because the mathematicians didn't want to explain it? Despite nearly all people who have just a highschool understanding of math have the gut-instinct to think 0.9999 recurring isn't 1? You say that the top tier of math-peoples actually agree with kids in their first year of highschool?

This is just surreal.

"You say that the top tier of math-peoples actually agree with kids in their first year of highschool?"

I didn't say they agree. I indicated they are appeasing those that cannot get past a difficult idea to grasp. This might sound a little condescending. But this thread is a clear example of people not being able to understand a certain limitation in the method of expressing real numbers without the use of fractions. If you don't understand this limitation, you will make mistakes like the mistakes we are seeing.

[SultanOfSurreal]

I didn't say they agree. I indicated they are appeasing those that cannot get past a difficult idea to grasp. This might sound a little condescending. But this thread is a clear example of people not being able to understand a certain limitation in the method of expressing real numbers without the use of fractions. If you don't understand this limitation, you will make mistakes like the mistakes we are seeing.

ok so there is a conspiracy by mathematicians to tell laymen, who think .999... only approaches 1, that .999... is exactly 1, because .999... only approaches 1 and this is too difficult for laymen to understand

this makes sense

[TheProwler]

It seems quite obvious that Prowler is the one who doesn't understand infinity.

Do you see that last one? It is not a 3. It is a 3 and one third. If you need to go a hundred decimal places, or a thousand, or a million, or as many as humanly possible, the only way to break it down (yo yo homie) is to make the last one "three and one third multiplied by 1/10^x" where x is a really big integer.

The last digit is not 3 and 1/3 multiplied by a really small number. Just as the last digit is not a 3. There is no last digit because it repeats infinitely.

You could say the last digit is 3*(1/10)^infinity. That is true, and its the same as saying there is an infinite chain of 3's

if you keep adding an extra 3 and doing this for days, weeks, months, years, centuries...you still won't have reached 4 inches...and you never will (assuming you are exact). BUT!!! If back when you were asked to move your thumb and finger apart 0.3333333 of a foot, we said 0.333333 plus (3 1/3) / 10 000 000 of a foot, you could have just moved your fingers 4 inches apart and called it a day. Because 0.333333 plus (3 1/3) / 10 000 000 is equal to 1/3.

This is very confusing to me. 0.3333recurring is exactly equal to 1/3.

0.333333 plus (3 1/3)/10 000 000 is not equal to any meaningful number.

You might have meant to say 0.3333recurring plus (3 1/3)/infinity = 1/3. That I can agree with, as it is the same statement, though more asinine. I find it strange that you take such care to state recurring when you want the number to be recurring, but in this case you neglected it and you represented infinity by a finite and relatively small number.

0.33333recurring = 1/3
0.99999recurring = 1/9

Good job on the 0.9999recurring equal 1/9. Try 0.1111recurring...but an honest mistake. Not a biggie.

In the rest of your post, you just demonstrated the deficiency in the way we attempt to represent numbers like 1/3 without using fractions. I was showing you how the only way to truly represent 1/3 accurately, is to use a fraction *somewhere*.

Why am I trying to explain this? There are a very small number of people that will understand. I do. Most don't. That's a given.

[Snorri1234]

I am quite sure, now that I see how difficult it is for people to get their heads around 0.333recurring and proper the proper use of arithmetic on numbers expressed this way, that this has been the motivation for mathematicians to just announce 0.999recurring equals 1 - to be done with it and start to get some work done. Or, maybe it is just the very top tier that have had to say "Shit, let's drop it. You're never going to understand."

So wait....wait wait...this is actually hilarious. So wait...

You claim that 0.9999 recurring was made 1 because the mathematicians didn't want to explain it? Despite nearly all people who have just a highschool understanding of math have the gut-instinct to think 0.9999 recurring isn't 1? You say that the top tier of math-peoples actually agree with kids in their first year of highschool?

This is just surreal.

"You say that the top tier of math-peoples actually agree with kids in their first year of highschool?"

I didn't say they agree.

You didn't say it, but it sure looks exactly the fucking same from over here.

I indicated they are appeasing those that cannot get past a difficult idea to grasp.

Yeah but dude, the thing is that they actually aren't appeasing them. People who can't grasp that .999 is one are normal regular people like freshmen math-students. You're saying and implying and whatever term that doesn't allow you to weasel out that the ones they are telling this lie are exactly the ones who would agree with them if they told the truth.

This might sound a little condescending.

Don't worry, you always sound like that.

But this thread is a clear example of people not being able to understand a certain limitation in the method of expressing real numbers without the use of fractions. If you don't understand this limitation, you will make mistakes like the mistakes we are seeing.

Actually, without meaning to sound condescending*, this thread shows most people actually understand that .999... represents a limit and not whatever you've got in your head. It honestly shows that people understand what a real number is.


*Actually do mean to sound condescending, i'm phat like that.

[Snorri1234]

I didn't say they agree. I indicated they are appeasing those that cannot get past a difficult idea to grasp. This might sound a little condescending. But this thread is a clear example of people not being able to understand a certain limitation in the method of expressing real numbers without the use of fractions. If you don't understand this limitation, you will make mistakes like the mistakes we are seeing.

ok so there is a conspiracy by mathematicians to tell laymen, who think .999... only approaches 1, that .999... is exactly 1, because .999... only approaches 1 and this is too difficult for laymen to understand

this makes sense

It's obvious isn't it? They tell people what they think is right is wrong, because what they think is right is right.


Yeah, I'm not sure I'm following the twisted, warped mind that comes up with these things.....

[Minister Masket]

I have better things to do with my time than worry about whether 0.999 recurring equals bloody 1 or not.
C'mon, does it really matter either way?

[bedub1]

so does .8999999999999... equal .9?

[thegreekdog]

Wait... I read these things. Is 1/9 really 0.999999999 etc.?

[Snorri1234]

I have better things to do with my time than worry about whether 0.999 recurring equals bloody 1 or not.
C'mon, does it really matter either way?

Since it pertains to some very fundamental parts of math, I'd say yes.


Now, whether we should argue about this on an internet-forum is a different matter. At least it passes the time...

[Snorri1234]

Wait... I read these things. Is 1/9 really 0.999999999 etc.?

Nah, sully just made a big mistake which I called attention to way before prowley did.

[StiffMittens]

I have better things to do with my time than worry about whether 0.999 recurring equals bloody 1 or not.
C'mon, does it really matter either way?

Does it matter?!! Are you saying you don't care if something infinitely tiny exists or not? At the end of the movie "The Incredible Shrinking Man" the protagonist asserts that no matter how small, he still exists. He still loved his wife, and even though he was becoming like a virus to her, she still loved him. Are you saying that doesn't matter?

[TheProwler]

Think of it as
10x - x = 9.00000...0000001

but it isn't.

0.9999... and 9.9999... have the SAME number of places after the decimal, so each one cancels out the other, when they are subtracted. THERE IS NO REMAINDER.

Haha, now you are defining infinity as a real number. "the SAME number"

So should we also say that in this equation, y = 1/x, that when x equals infinity (haha, x equals infinity), y=0? Don't answer that...I think we'd be into a whole new (and related) subject with people not understanding the limitations of performing basis algebra on non-real numbers.

[owheelj]

Yes it does. [edit; 0.8999... = 0.9] - there are numerous mathematical proofs and concepts (such as some fractals) that rely on this fact.

There is no conspiracy from mathematicians. They all agree that 0.9 recurring is equal to 1. There are numerous proofs. I've provided the simplest and easiest to understand, but there are others.

I suggest everybody who doesn't believe it go read the wikipedia article, and if you don't think that's a reliable source, go read the 50 or so maths text books it refers to. Don't post your disagreement until you've read the article in full and those text books, because you're opinions really based on your misunderstanding of mathematical concepts based on your ignorance, and not on reality. This is a dumb argument to be having, because one side is clearly proven and the other is not. It's a debate between those who understand maths and those who think they know more about maths than maths, which doesn't even make sense.

[InkL0sed]

I have better things to do with my time than worry about whether 0.999 recurring equals bloody 1 or not.
C'mon, does it really matter either way?

Does it matter?!! Are you saying you don't care if something infinitely tiny exists or not? At the end of the movie "The Incredible Shrinking Man" the protagonist asserts that no matter how small, he still exists. He still loved his wife, and even though he was becoming like a virus to her, she still loved him. Are you saying that doesn't matter?

VIRUS

string

[TheProwler]

I didn't say they agree. I indicated they are appeasing those that cannot get past a difficult idea to grasp. This might sound a little condescending. But this thread is a clear example of people not being able to understand a certain limitation in the method of expressing real numbers without the use of fractions. If you don't understand this limitation, you will make mistakes like the mistakes we are seeing.

ok so there is a conspiracy by mathematicians to tell laymen, who think .999... only approaches 1, that .999... is exactly 1, because .999... only approaches 1 and this is too difficult for laymen to understand

this makes sense

Well, I wouldn't call it a conspiracy. I would call it an understanding of the limitations of most people's ability to grasp certain concepts and an attempt to get past a fairly trivial matter.

[Snorri1234]

Think of it as
10x - x = 9.00000...0000001

but it isn't.

0.9999... and 9.9999... have the SAME number of places after the decimal, so each one cancels out the other, when they are subtracted. THERE IS NO REMAINDER.

Haha, now you are defining infinity as a real number. "the SAME number"

So should we also say that in this equation, y = 1/x, that when x equals infinity (haha, x equals infinity), y=0? Don't answer that...I think we'd be into a whole new (and related) subject with people not understanding the limitations of performing basis algebra on non-real numbers.

Actually, Timminz is so motherfucking right it isn't even funny anymore. Infinity is always the same.

also yeah, y= 1/x with x being infinity does make y=0. Not that you didn't know that, but I always like to tell trolls facts.