.999... = 1

[TheProwler]

I never claimed 3.333 recurring x 3 = 9 and not 10. I claimed that 3+3+3=9. Do you disagree with this?

If the current mathematical community has decided that this argument needed to be settled with a simple explanation so students can move on a learn new things, so be it.

There have been proofs of this for well over 200 years, probably a lot longer.

Watch this;


3*3=9
3.3*3=9.9
3.33*3=9.99
3.333*3=9.999
3.3333*3=9.9999
3.33333*3=9.99999
3.333333*3=9.999999
3.3333333*3=9.9999999
3.33333333*3=9.99999999
3.333333333*3=9.999999999
3.3333333333*3=9.9999999999
3.333... 100 3s... 333*3=9.999...100 9s... 999

therefore
3.333... infinite 3s... 333*3=9.999... infinite 9s... 999

With all due respect, you do not understand. You are recognizing a pattern when dealing with a finite degree of accuracy. But when dealing with an infinite degree of accuracy, your pattern is invalid. Because that last "3" on the right is not really a 3. It is a 3 1/3. You showed a degree of accuracy of 106 decimal places. That is not very close to infinity (haha). To understand this, just change that last 3 to a 3 1/3.

3 1/3 * 3 equals 10, not 9.

I already said this, you just don't seem to understand. I am not going to keep trying to explain it.

The weakness in the math is the simple fact that one cannot properly represent one third as a real number without showing it as a fraction. 0.333recurring is not cutting it for you and others, clearly. Because you are not grasping the idea of infinity. So it would be better to display the number this way: 1/3

And you wonder why mathematicians have decided to teach students of math that 0.999recurring equals 1? It's just easier that way. And, like I said before, in practical terms, thinking this way does no real harm. Well, it may be somewhat harmful - you might start to think things like "If I plug x=infinity into the equation y=x^-1, I'll get a result of y equals zero." And everybody knows that you have to plug in x=infinity squared to get y=0. Haha, just kidding.

Someday you might understand that 0.999recurring approaches 1, but never equals one. And you possibly never will understand it. Not a big deal.

[jonesthecurl]

It's odd that nobody has objected to the notion of .33 recurring being exactly one third, and yet multiplying it by 3 makes it untrue.

Also, nobody liked my triangle story?

[Snorri1234]

It's odd that nobody has objected to the notion of .33 recurring being exactly one third, and yet multiplying it by 3 makes it untrue.

I find it especially odd that nobody has figured to point out that Prowler is misrepresenting the stances. In a rather absurd way.

Namely:
3 1/3 * 3 equals 10, not 9.

I mean, it seems to be smart and all but it's actually nonsense. He's asking us to replace the last 3 with 3 1/3 yet just skips over the fact that that last 9 is also not just a 9.


It's a rather interesting way to troll, and it seems to work.

[TheProwler]

It's odd that nobody has objected to the notion of .33 recurring being exactly one third, and yet multiplying it by 3 makes it untrue.

I don't object to it because it is correct. Other people are having a hard time multiplying .333recurring properly.

Also, nobody liked my triangle story?

"4 jones in a box"? Like a little family of joneses.

[Snorri1234]

Nah prowly, it's more that jones wonders why one would accept that .333 recurring is one third and not accept that .999recurring is 1.

Because .3333recurring to infinity has exactly the same problem as .999recurring to infinity which you seem to have with it. According to you, it approaches 1/3 but it will never be it.

[TheProwler]

It's odd that nobody has objected to the notion of .33 recurring being exactly one third, and yet multiplying it by 3 makes it untrue.

I find it especially odd that nobody has figured to point out that Prowler is misrepresenting the stances. In a rather absurd way.

Namely:
3 1/3 * 3 equals 10, not 9.

I mean, it seems to be smart and all but it's actually nonsense. He's asking us to replace the last 3 with 3 1/3 yet just skips over the fact that that last 9 is also not just a 9.


It's a rather interesting way to troll, and it seems to work.

Ahhh, see, with an infinite number of 3's, there is no last 3.

So let's say you go display the number this way: 0.333recurring

What this breaks down to is this:

0 * 1 plus
3 * 1/10 plus
3 * 1/100 plus
3 1/3 * 1/100

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.

You can try to write out an infinite amount of 3's if you think that will help you get it. Get it?

[TheProwler]

Nah prowly, it's more that jones wonders why one would accept that .333 recurring is one third and not accept that .999recurring is 1.

Because .3333recurring to infinity has exactly the same problem as .999recurring to infinity which you seem to have with it. According to you, it approaches 1/3 but it will never be it.

Absolutely wrong.

.333recurring equals 1/3

.999recurring does not equal 1 (just as it does not equal 3 times .333recurring)

[jonesthecurl]

..and by the time the athlete reaches the point at which the turtle was just now,it's moved again. You can never catch the tortoise.
Except you can.

[Snorri1234]

It's odd that nobody has objected to the notion of .33 recurring being exactly one third, and yet multiplying it by 3 makes it untrue.

I find it especially odd that nobody has figured to point out that Prowler is misrepresenting the stances. In a rather absurd way.

Namely:
3 1/3 * 3 equals 10, not 9.

I mean, it seems to be smart and all but it's actually nonsense. He's asking us to replace the last 3 with 3 1/3 yet just skips over the fact that that last 9 is also not just a 9.


It's a rather interesting way to troll, and it seems to work.

Ahhh, see, with an infinite number of 3's, there is no last 3.

And with an infinite number of 9's , there is no last 9.

[Falkomagno]

touché

[TheProwler]

And with an infinite number of 9's , there is no last 9.

That's right. And 0.999recurring still doesn't equal 1.

Let me try to help...let's take a few numbers and multiply them...

175 * 5 = 875

Lets solve it this way

175
5
-----
5 (5 * 5 is 25, write down 5 and carry the 2)
75 (5 * 7 is 35 plus the 2 carried is 37, write down the 7 and carry the 3)
875 (5 * 1 is 5 plus the 3 carried, write down the eight)

What are you noticing? That results on digits to the right can affect their "neighbouring" digit on the left. Where you place the decimal point is not gonna matter. So, the problem with 0.333recurring is that there is always a digit on the right. You can't ever get to the last digit to see how much is being carried over. The only way to do this (am I repeating myself?) is to understand that you need to use a fraction to properly represent 0.333recurring. That fraction is 1/3.

I said it before, the problem is that 0.333recurring doesn't represent the number in a way that you are able to wrap your head around it. You don't really grasp the idea of infinity.

I really don't know how to help you understand. Let's say we do this...a foot is 12 inches...so 1/3 of a foot is 4 inches....now if you are asked to hold your thumb and finger apart 4 inches, you can do it....(let's say you are able to do this very precisely - no coffee for you)....if you are asked to hold you thumb and finger apart 1/3 of a foot, you can do it (it is equal to 4 inches)....if you are asked to hold your thumb and finger apart 0.33333 of a foot, you can do it. But that is less than 1/3. So we get more precise - 0.333333 of a foot...your finger moves very slightly....0.3333333 of a foot....your finger mores even slightlier ( )...and as we keep adding 3's....your finger continues to move more slightly and more slightly...but it keeps moving....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.

To be crystal clear: 3 * 0.333recurring does not equal 0.999recurring. Whether you do addition or multiplication, you are forgetting to carry numbers.

Just use fractions, because you understand them.

I have to stop this now, because, seriously, there are things I understand that others do not and it is impossible to explain it in a way that they will understand.

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 I have to say:

Shit, let's drop it. You're never going to understand.

[Timminz]

if, x=0.999...

then, 10x=9.999...

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

QED

[InkL0sed]

So I have to say:

Shit, let's drop it. You're never going to understand.

QED

[jonesthecurl]

if, x=0.999...

then, 10x=9.999...

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

QED

Our teachers told us that Q.E.D. stood for Quod Erat Demonstrandum ("that which was to be shown").
We always said it stood for Quite Easily Done.

[Snorri1234]

Yay me for going to entertain the troll.

And with an infinite number of 9's , there is no last 9.

That's right. And 0.999recurring still doesn't equal 1.

So why is .333 recurring 1/3 then?

By you own logic .333recurring will only approach 1/3, not be it.

Let me try to help...let's take a few numbers and multiply them...

175 * 5 = 875

Lets solve it this way

175
5
-----
5 (5 * 5 is 25, write down 5 and carry the 2)
75 (5 * 7 is 35 plus the 2 carried is 37, write down the 7 and carry the 3)
875 (5 * 1 is 5 plus the 3 carried, write down the eight)

What are you noticing?

That you seem to think I don't understand basic math?

What are you noticing? That results on digits to the right can affect their "neighbouring" digit on the left. Where you place the decimal point is not gonna matter. So, the problem with 0.333recurring is that there is always a digit on the right. You can't ever get to the last digit to see how much is being carried over. The only way to do this (am I repeating myself?) is to understand that you need to use a fraction to properly represent 0.333recurring. That fraction is 1/3.

You don't need the fraction to properly represent it, you just need the fraction to make it easier to understand and workable for using.

I said it before, the problem is that 0.333recurring doesn't represent the number in a way that you are able to wrap your head around it. You don't really grasp the idea of infinity.

You don't either. Nobody does, it's why math is so hilarious.

I really don't know how to help you understand. Let's say we do this...a foot is 12 inches...so 1/3 of a foot is 4 inches....now if you are asked to hold your thumb and finger apart 4 inches, you can do it....(let's say you are able to do this very precisely - no coffee for you)....if you are asked to hold you thumb and finger apart 1/3 of a foot, you can do it (it is equal to 4 inches)....if you are asked to hold your thumb and finger apart 0.33333 of a foot, you can do it. But that is less than 1/3. So we get more precise - 0.333333 of a foot...your finger moves very slightly....0.3333333 of a foot....your finger mores even slightlier ( )...and as we keep adding 3's....your finger continues to move more slightly and more slightly...but it keeps moving....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.

I can actually completely exactly gauge 4 inches by hand.

To be crystal clear: 3 * 0.333recurring does not equal 0.999recurring. Whether you do addition or multiplication, you are forgetting to carry numbers.

That's quite a leap you made from your "proof" there.

Just use fractions, because you understand them.

Ah, this is too complex! That's it! You don't actually have to make any sense, you can just say "it's too complex dude".

I have to stop this now, because, seriously, there are things I understand that others do not and it is impossible to explain it in a way that they will understand.

I AM TOO SMART TO EXPLAIN THINGS! JUST TOO DAMN SMART! ALL YOU OTHER PEOPLE WITH YOUR FANCY UNDERSTANDING OF MATH JUST DON'T UNDERSTAND HOW SMART I AM!

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.

[Snorri1234]

if, x=0.999...

then, 10x=9.999...

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

QED

Our teachers told us that Q.E.D. stood for Quod Erat Demonstrandum ("that which was to be shown").
We always said it stood for Quite Easily Done.

Actually, it stand for Quite Easily Done but the mathematicians figured you wouldn't understand that so they told you it was Quod Erat Demonstrandum.

[InkL0sed]

Dude, it's like so totally obvious, just look at it this way dude.

If you take 9/10s, and then 9/10ths of the 1/10th left, and keep doing that no matter how many times, you never get all the way to 1 dude! I mean it's like a simple concept dude, that's why .999... doesn't equal 1, cause it like, never gets the whole way there man.

[sully800]

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 = 3/3 = 1



*edited my typo

[Falkomagno]

yeah. the thing is that prowler doesn't know that 0.999... is a notation, a way to describe, and is exactly 1. "0.999..." represents "one" as "1" as well. More of that it's just blah blah blah

1/3= 0.333...="one third"= 0.333 recurrent. Period

[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

[InkL0sed]

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 is no "last digit" of .333...

That's what the ellipsis means.

[SultanOfSurreal]

will you people please stop talking about the last digit in a number that has no last digit

it is embarrassing

ps prowler is a retard no joke

[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 is no "last digit" of .333...

That's what the ellipsis means.

i know...there isn't anything as infinity+1 either. But that helps the people who don't realize that there is no last digit...thus realize that it's all just really 1/3rd....so when they get to the "last digit" in their mind, they can finally make the equation whole....cause three 1/3rds everybody agrees is 1, so now they have a 1 to carry all the way through all the 3's to get to the result of 1.

[SultanOfSurreal]

I have to stop this now, because, seriously, there are things I understand that others do not and it is impossible to explain it in a way that they will understand.

lol says the person whose education in math obviously ended sometime around high school, who describes problems regarding recurring numbers in terms of how third graders add and multiply integers, and who thinks drawing an incredibly stupid analogy to a person performing a finite process says anything whatsoever about infinity

[Snorri1234]

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

I think I might have spotted a mistake there sully dear chap.