But there is no illusion.
1/3 does not equal .3333
1/3 is a whole fraction, .3333 is a recurring decimal, they are not equal.
1/3 does not equal .3333
1/3 is a whole fraction, .3333 is a recurring decimal, they are not equal.
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But there is no illusion.
1/3 does not equal .3333
1/3 is a whole fraction, .3333 is a recurring decimal, they are not equal.
1/3 is the fractional representation of .3333...
If I take 3*(1/3), I get 3/3 which is 1.
But there is no illusion.
1/3 does not equal .3333
1/3 is a whole fraction, .3333 is a recurring decimal, they are not equal.
No, words mean things.
0.333... Is the decimal equivalent of 1/3.
It's an artifact of an irrational result.
But it is most certainly 1/3.
The one sure way to get 0.333... is to carry out the mechanics of actually dividing 1 by 3 until you're done.
(1/3) * 3 = 1
Every time.
Because ((1/3) * 3) = (1 * (3/3)) = (1 *1) = 1
So when 1/3 * 3 does not equal 1, that's the day when 0.999... does not equal 1.
No mathematician ever looks at 0.333... and wonders what it means.
It means 1/3.
Hope this helps.
jhawkkw
Chinchillin'
And to make the whole argument even richer, this idea expands to other numbers. For example, .199999..... is actually .2. It's not as easy to find the arithmetic proof show above using 1/3, but the algebraic, calculus through infinite series, and analysis proof by contradiction all fall in line and take similar trend that the .999...=1 proof does.
jhawkkw
Chinchillin'
A valid proof, there's lots of mathematical "proofs" out there that show things to be true even though everyone knows them to be false. This is done by breaking rules of mathematics like division by zero, using invalid domains, etc. These are what we call mathematical fallacies.
Shall I start a new thread for "1.999... = 2"?
:rofl:Seriously, though, this is a great thread--evoking lots of thought and discussion for a topic I never thought would get past the first page
.
jhawkkw
Chinchillin'
Shall I start a new thread for "1.999... = 2"?
Seriously, though, this is a great thread--evoking lots of thought and discussion for a topic I never thought would get past the first page
Yeah, a math topic on an android website is epic.
Shall I start a new thread for "1.999... = 2"?
Seriously, though, this is a great thread--evoking lots of thought and discussion for a topic I never thought would get past the first page
Actually, it's been pretty we well covered by two posts from the front page -
M
Member243850
Guest
You are right it is very strange actually!
Me too!
I think what happens is that we (maybe only me because of me low IQ?
) don't know how to write in decimal notion the value of a third or 1/3.We can imagine it in our heads / craniums and you can imagine 1/3 in your head but I think there is some kind of problem when you start to make an equation like:
1/3 = 0.33333333333
And so on and so on.
If you take:
1/3 * 3 = 1
There is no problem here because we don't use decimals!
But 0.99999999 reoccurring (going on forever) will never equal 1 in my books.
I think I may be wrong or right?
But I think I am on the right track.
You will always get closer to 1 but never get to 1.
I think the confusing part for many (maybe only me?
) is when you take a third (or 1/3) and you turn it into decimals because you can't like happily (if I it is okay to use this word! ) demonstrate this as If you say a quarter just for example or some other "even" fraction then that is different story I think!
1/4 = 0.25
Now if you times 0.25 by 4 you will happily without any issues get a whole or 1.
But I think it is just that because of the "odd" fraction trying to write it out into a 100 makes it harder than the bog standard and easy 1/4 just for example.
A third totally exists!
No doubt about it!
But I think it is difficult to demonstrate a 1/3in decimal notation.
A 1/3 just doesn't like to show up "happily" when decimals are used.
At least that is what I think!
It has to equal 1.
The only accurate way to represent one third is 1/3.
If you do the math you get -
0.333... where the 3s go on forever.
It's not an approximation - 0.333... is called the decimal equivalent of 1/3.
Equivalent - it means: same exact thing.
If the world was decimal only, it would take you an infinite time to cut a pie into thirds.
But you don't need an infinite time to cut a pie into thirds. Even if you think decimal.
That's reality.
Math is a way to describe reality.
0.333... and 1/3 both describe the same exact reality.
And so 0.999... is 1 in the same way.
One of those is the thing, the other is its decimal equivalent.
In other words, the same exact thing.
We don't get to vote on French. In that language, oui means yes. It doesn't mean another word.
In the language of mathematics, 0.999... means 1.
Just like French, it's not open to a vote, and it doesn't mean something else.
Avoid pie cutting jokes and sophistry about what yes means, and it'll help make the situation clear.
Despite what others are saying, 0.999... is not almost 1.
It's the same exact thing.
Just as words mean things, so do various math terms.
Hope this helps.
M
Member243850
Guest
But that statement actually proves that .9999... will never, ever, ever become 1.
.9999... does not and will never = 1
1 is an integer, .9999... is not, and will never become, an integer.
If you subtract .9999... from 1 there will always be a remainder, no matter how infinitesimally small.
I totally agree actually!
This so called "proof" over here is actually not correct and is actually bogus:
x = 0.999... (going on forever but must stop somewhere to prove it)
10x = 9.999...
10x - x = 9.999... - 0.999 (this is where I have a problem when they claim they have subtracted the original x but they actually have not. You just can't see it, but I will show you!
) 9x = 9 (it actually doesn't because you have not subtracted the original x and will show you why later)
x = 1
Well this proof is not true actually at all, I don't care if it is on Wikipedia because they are not God and don't know everything.
Many articles on Wikipedia are edited by psycho paths so I don't agree with many of their stuff and who says things can't change?
People said the earth was flat and if you disagreed you were laballed insane... so why can't I disagree and show you a good reason why do?
I will show you why this proof is wrong actually.
You can say 0.99999... goes into infinity ... BUT you have to stop some where to make x "stable" and even or the same because you need to make the original x the same as it was in the beginning.
It won't make any sense if you just carry on going on into infinity ... you need to make both x the same!
For example let us just say we only go to the 10th decimal after the comma or decimal starts etc so I can prove to you in a simpler way.
We will only take the 10th decimal here and not make it "look" fancy like it does from the said example that people believe is true
Here:
x = 0.9999999999 (we only go to the 10 decimal place and not any further because there is no need to!
)let us multiply both sides by 10 like in the so called "proof"...
10x = 9.999999999 (now there are only 9 decimals after the whole 9 when we times both sides by 10 do it on your calculator if you do not believe me!
It is no longer 10 decimals after the comma!)Now they claim you just minus the original x from both sides because what you do to one side you must do to the other.
10x - x = 9.999999999 - 0.9999999999
Now if you simply take:
9.99999999 - 0.999999999
you will get:
8.9999999991
You will not have:
9x = 9
You should have:
9x = 8.9999999991
I just think people don't realise you can't write 1/3 or 2/9 and make 1 usng decimals!
At least that is how I see it!
Lordvincent 90
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
But the reality is it doesn't stop... That's how a repeating decimal works. It is infinite. Using your same logic, please explain to me the 'appropriate' place to stop in pi (not a repeating decimal but still considered to be infinite)
M
Member243850
Guest
It has to equal 1.
The only accurate way to represent one third is 1/3.
If you do the math you get -
0.333... where the 3s go on forever.
It's not an approximation - 0.333... is called the decimal equivalent of 1/3.
Equivalent - it means: same exact thing.
If the world was decimal only, it would take you an infinite time to cut a pie into thirds.
But you don't need an infinite time to cut a pie into thirds. Even if you think decimal.
That's reality.
Math is a way to describe reality.
0.333... and 1/3 both describe the same exact reality.
And so 0.999... is 1 in the same way.
One of those is the thing, the other is its decimal equivalent.
In other words, the same exact thing.
We don't get to vote on French. In that language, oui means yes. It doesn't mean another word.
In the language of mathematics, 0.999... means 1.
Just like French, it's not open to a vote, and it doesn't mean something else.
Avoid pie cutting jokes and sophistry about what yes means, and it'll help make the situation clear.
Despite what others are saying, 0.999... is not almost 1.
It's the same exact thing.
Just as words mean things, so do various math terms.
Hope this helps.
I disagree!
Why?
9x=9
It's correct because math with infinities works.
If it didn't, modern electronics wouldn't exist.
You don't get to stop at a certain point on the way to infinity.
Infinity times any integer except 0 is an infinity.
Every time.
Usually you can get stuck there.
But you can make two infinities cancel each other out, so you can put the problem on the right track.
That's exactly why 9x=9.
Because that's how infinity works.
Not because Wikipedia said so and you can vote on Wikipedia.
And sometimes, where the decimal expression isn't there, you can get the decimal equivalent.
The same exact thing.
It's correct because math with infinities works.
If it didn't, modern electronics wouldn't exist.
You don't get to stop at a certain point on the way to infinity.
Infinity times any integer except 0 is an infinity.
Every time.
Usually you can get stuck there.
But you can make two infinities cancel each other out, so you can put the problem on the right track.
That's exactly why 9x=9.
Because that's how infinity works.
Not because Wikipedia said so and you can vote on Wikipedia.
And sometimes, where the decimal expression isn't there, you can get the decimal equivalent.
The same exact thing.
Ok, fair enough.
If math terms can mean anything you like, then words can mean anything I like.
Thank you for saying that you agree with me!
M
Member243850
Guest
Well why should you be repeating on going on into infinity in the first place?
Why do you need to go on into infinity anyway?
Why is the "reality" is it "never stops"?
Why do you not need to stop?
1 is not infinite.
It is 1.
Why should you even have to bother keep on repeating it (0.999999...) if it already equals 1?
Why?
You should not have to repeat anything at all.
1 = 1
and not
1 = 0.999999999
It is simple.
They are not equal at all.
Not 1 bit.
No matter how far you go you will never get to 1.
Ever.
1 = 1
And not
1 = 0.9999
Or
1 = 0.99
No not true.
Pi is just another good example of exactly what I was trying to say about how we struggle to write some (maybe many many many?) fractions into decimal notation.
Pi is just another fraction and also shows how much we struggle to write many things in decimal notation.
Pi is proof of what I am trying to say actually!
B
Bamboosaurus
Guest
I've always seen it as .99999... = 1 at infinity. So the limit is 1.
@Stinky stinky, though the method you posted works for a finite number, it doesn't work because there are an infinite numbers of 9s after the decimal point. Moving the decimal point over one doesn't suddenly make it have 1 less than infinity. Infinity - 1 = infinity.
@Stinky stinky, though the method you posted works for a finite number, it doesn't work because there are an infinite numbers of 9s after the decimal point. Moving the decimal point over one doesn't suddenly make it have 1 less than infinity. Infinity - 1 = infinity.
Pi cannot be represented with any fraction.
It's not the same thing as a third.
All we can do with pi is represent an approximation of it to some degree.
Yet - despite pi not being any fraction, and not being able to even completely represent it - circles exist anyway.
And you cut one of those circles into thirds you'll always have all of the circle.
It'll just be in pieces.
You won't suddenly have almost almost a whole circle if you translate this post into French.
And you won't have almost a circle when clumsy arithmetic tells you that you ended up with 0.999... circles.
It's not the same thing as a third.
All we can do with pi is represent an approximation of it to some degree.
Yet - despite pi not being any fraction, and not being able to even completely represent it - circles exist anyway.
And you cut one of those circles into thirds you'll always have all of the circle.
It'll just be in pieces.
You won't suddenly have almost almost a whole circle if you translate this post into French.
And you won't have almost a circle when clumsy arithmetic tells you that you ended up with 0.999... circles.
B
Bamboosaurus
Guest
Well why should you be repeating on going on into infinity in the first place?
Why do you need to go on into infinity anyway?
Why is the "reality" is it "never stops"?
Why do you not need to stop?
1 is not infinite.
It is 1.
Why should you even have to bother keep on repeating it (0.999999...) if it already equals 1?
Why?
You should not have to repeat anything at all.
1 = 1
and not
1 = 0.999999999
It is simple.
They are not equal at all.
Not 1 bit.
No matter how far you go you will never get to 1.
Ever.
1 = 1
And not
1 = 0.9999
Or
1 = 0.99
No not true.
Pi is just another good example of exactly what I was trying to say about how we struggle to write some (maybe many many many?) fractions into decimal notation.
Pi is just another fraction and also shows how much we struggle to write many things in decimal notation.
Pi is proof of what I am trying to say actually!
Pi is not a fraction. It numbers at the end do not reach an end and don't have a pattern. Unless of course you mean pi/1.
1 = 1.00000...
2 = 2.00000...
3 = 3.00000...
As you can see from the above, every integer MUST have an infinitely repeating pattern of zeros after the decimal point
B
Bamboosaurus
Guest
I think the problem is that some people don't quite fully understand what infinity is. Once early calculus (limits and such) is learned the proofs will make sense.
M
Member243850
Guest
Ok, fair enough.
If math terms can mean anything you like, then words can mean anything I like.
Thank you for saying that you agree with me!
Le sigh!
How childish of you EarlyMon!
I did not think this of you!
And no!
I don't agree with you at all!
So EarlyMon... you are saying that... things can never change and whatever the flawless scientists say... it is set in stone forever???
Why can't things change???....
Are you saying this so called "proof" can never change?
You did not even look at what i was trying to say!
You claimed I "believe maths terms can mean anything I like"..????
I did not mean that at all buddy!
Sorry!
Where did you get that from?
Why can't some one question things????
Isn't this how the light bulb was made and the computer you are typing from???
You do know that the so called "scientists" from 1000's or whatever of years ago "knew" that the Earth was "flat"...
They "knew"...
They were wrong.
Very very wrong.
The so called "top scientists" were arrogant idiots...
Things change... times they change and people they change.
Everything changes over time...
Theories change...... it is how we move forward... and question things... not go backwards...
You did not get what I was trying to say!
I disagree with what you guys are saying and I am cool with this.
I don't agree with it...
I have said what I wanted to say and I am sticking to it thanks!
I guess I am like this guy sometimes in this cartoon... awesome cartoon...
