0.9999....(recurring) = 1?

George,Y · 2006-12-25 17:04:54

I used the gasoline example just to demonstrate the occasions when we think infinite digits as exact and in fact they are not. Or put another way, we tend to over-believe in infinite digits, for they appear more accurate than simply 3 or 4 digits- but are they generally more correct than sufficient large digits( e.g. 10[sup]24[/sup] digits in the gasoline estimation) ?

Anthony.R.Brown · 2007-01-02 01:43:00

To Ehiness

Quote
Ok I am 99.999...% sure that you have no idea what infinite means.

I am 1% more sure than you that I have more idea what Infinte means,that makes 100%,which is greater than any Infinite Number.

Anthony.R.Brown · 2007-01-02 01:51:35

To Devanté

Quote
Anthony, 0.333..., as you said (I think), multiplied by 3, is 0.999... . Now, 1/3 multiplied by 3 is 3/3, right? If 1/3 = 0.333..., tell me what you answer is when you multiply that my 3. And stop straying from the answer.

3 x Infinite 0.3 ( If it was possible? ) = 0.9999........ /3 = 0.333... multiply that my 3 = 0.9999........

Ricky · 2007-01-02 05:31:39

3 x Infinite 0.3 ( If it was possible? ) = 0.9999........ /3 = 0.333... multiply that my 3 = 0.9999........

Correct. Now you've also said that Infinite 0.3 = 1/3. And so 1/3 * 3 = 1.

1/3 = Infinite 0.3 #Now multiply both sides by 3
1/3 * 3 = Infinite 0.3 * 3
1 = 0.999999.....

So by your very own words, Anthony, you just prove what you have been saying is false.

Anthony.R.Brown · 2007-01-04 01:47:10

To Ricky

Quote:"Correct. Now you've also said that Infinite 0.3 = 1/3."

A.R.B I said if possible! Decimal 0.3 is not the same as 1/3

the same as 3 x Infinite decimal 0.3 is not the same as 3 x 1/3

Anthony.R.Brown · 2007-01-08 01:56:23

To George,Y

Quote: X'(y-Xβ)=0

can you explain this more! are you saying an Infinite Number is! or becomes Zero!?

George,Y · 2007-01-11 15:19:44

It's on linear algebra, nothing about infinite decimals.

MathsIsFun · 2007-01-11 16:38:56

Anthony.R.Brown wrote:

... the same as 3 x Infinite decimal 0.3 is not the same as 3 x 1/3

If you replace "Infinite" with "Finite" we can all agree

Infinite is not "big", it is endless. Nothing in our real world is like it. But it is a simple idea. It is simply "no end".

So there is no end to the "3"s in 0.333...

It doesn't end like ...33330 or anything weird, because there is no end. So there can be no "little bit at the end" to cause any inaccuracy.

But in the "finite" world you would be right. You can play with an example here: Base Conversion

Try entering "Ternary" 0.1, it will convert it to Decimal 0.333333. This looks right, but if you keep playing you will find it gets some things wrong as well, because it is only calculating to so many decimal places.

(Hey, we are on Page 10 of this discussion. I wonder how long it will take to get to Page 20? )

Anthony.R.Brown · 2007-01-12 01:45:04

To MathsIsFun Administrator

A = (1/3) This is not Infinite! just 1 3rd of a whole Number!

B = 1/3

B = 0.333333333333333333................This is Infinite! (or as you say "Infinite is not "big", it is endless." )

B x 3 = 0.999999999999999................This is Infinite! (or as you say "Infinite is not "big", it is endless." )

Ricky · 2007-01-12 06:26:02

ARB, are you under the impression that 0.3333333.... is an infinitely large number? Can you answer me this? Is 0.33333.... > 0.4?

Devantè · 2007-01-12 08:11:38

If you rubbed out a bit of the 4 to make a 1, then yes.

Last edited by Devanté (2007-01-12 08:11:53)

George,Y · 2007-01-12 16:51:48

Anthony.R.Brown wrote:

To MathsIsFun Administrator
A = (1/3) This is not Infinite! just 1 3rd of a whole Number!
B = 1/3
B = 0.333333333333333333................This is Infinite! (or as you say "Infinite is not "big", it is endless." )
B x 3 = 0.999999999999999................This is Infinite! (or as you say "Infinite is not "big", it is endless." )

Anthony is just protesting the idea to equate a simple and finite number 1/3 with a perplexing infinite expression of 0.333...

luca-deltodesco · 2007-01-12 20:18:24

and he is also trying to argue that 1/3 =/= (1/3), that putting brackets around it makes it different, because 1/3 = 0.333..., but (1/3) doesnt

Anthony.R.Brown · 2007-01-13 03:11:22

If i say A = (1/3) and A is not a decimal Calculation! then A must = one 3rd

If i say A = 1/3 and A is a decimal Calculation! then A must = 0.333333333......

Ricky · 2007-01-13 03:55:14

George,Y wrote:

Anthony.R.Brown wrote:
To MathsIsFun Administrator
A = (1/3) This is not Infinite! just 1 3rd of a whole Number!
B = 1/3
B = 0.333333333333333333................This is Infinite! (or as you say "Infinite is not "big", it is endless." )
B x 3 = 0.999999999999999................This is Infinite! (or as you say "Infinite is not "big", it is endless." )
Anthony is just protesting the idea to equate a simple and finite number 1/3 with a perplexing infinite expression of 0.333...

No George. That's what you're saying. ARB is allowing for infinite decimals, as can be clearly seen in the post you quoted. He's fine with an infinite decimal, but he somehow thinks that (1/3) is different from 1/3.

Anthony.R.Brown · 2007-01-13 03:56:54

B "is a Decimal Calculation"

B = 1/3

B Must Eqaul 0.33333333........

B x 3 Must Eqaul 0.99999.......

B Must be Infinite!

B Must be < 1

Ricky · 2007-01-13 04:06:43

B x 3 Must Eqaul 0.99999.......

But you also stated that B = 1/3

So B x 3 must equal 1/3 x 3. What does 1/3 x 3 equal? Simply put, 1/3 x 3 = 1.

Now we have B x 3 = 0.999... and B x 3 = 1/3 x 3 = 1. This must mean that 0.999... = 1, since 0.999... = B x 3 = 1/3 x 3 = 1.

Anthony.R.Brown · 2007-01-14 01:07:43

To Ricky

A = (1/3 x 3) = 1 "This is all part of the same Calculation! and so does = 1"

B = 1/3 = 0.333333....."This has now been Converted to Decimal! and lost its Accuracy!"
"i.e the Nearest Decimal to one 3rd can only be 0.3.. which is inaccurate! but important"

B x 3 = 0.9999...."This has now been Multiplied as Decimal! and has still lost its original Accuracy!"
"i.e the Nearest Decimal to one 1 can only be 0.9.. because of the Calculations that have been done! which is inaccurate! but important"

B has become Infinite 0.999...... "Because it is Inaccurate! but Nether less! and Most Important! permanently < 1

A - B must Equal 0.1 Because their Values have come from Different Calculation Accuracy's!

Devantè · 2007-01-14 06:44:42

I think that a moderator should close this thread or the other one, it seems we now have two threads that are dealing with the same identical thing.

Ricky · 2007-01-14 08:10:18

If you don't think that 1/3 = 0.333..., then why do you continuously post it?

B = 1/3
B Must Eqaul 0.33333333........

Edit: And if that's the case, then I retract what I said to George in my previous post. My apologies, but you have to understand that I am having a very difficult time understanding what ARB is trying to say.

Anthony.R.Brown · 2007-01-15 01:26:12

To Ricky!

A = 1/3 "If this is a Normal Calculation! then this Equals One 3rd"

B = 1/3 "If this is a Decimal Calculation! then this Equals 0.3 i.e NOT QUITE One 3rd!!"

Devantè · 2007-01-15 04:13:43

OK, now I think a mod should really close this thread. Duplicate posts are being created. Unnecessarily.

mathsyperson · 2007-01-15 05:10:48

OK fine. I'll close the other one though, because this one was the original.

Ricky · 2007-01-15 09:00:59

Anthony.R.Brown wrote:

To Ricky!
A = 1/3 "If this is a Normal Calculation! then this Equals One 3rd"
B = 1/3 "If this is a Decimal Calculation! then this Equals 0.3 i.e NOT QUITE One 3rd!!"

Sorry to burst your bubble ARB, but decimal calculations are defined in a very strict sense so that they behave exactly (no if's, and's or but's) as your "normal calculation".

Anthony.R.Brown · 2007-01-16 01:04:55

To Ricky!

A = 0.3

B = 0.3

C = 0.3

A + B + C = 0.9

Can you show me the Value that needs to be add in this Calculation! to make A + B + C = 1

Math Is Fun Forum

#226 2006-12-25 17:04:54

Re: 0.9999....(recurring) = 1?

#227 2007-01-02 01:43:00

Re: 0.9999....(recurring) = 1?

#228 2007-01-02 01:51:35

Re: 0.9999....(recurring) = 1?

#229 2007-01-02 05:31:39

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#230 2007-01-04 01:47:10

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#231 2007-01-08 01:56:23

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#232 2007-01-11 15:19:44

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#233 2007-01-11 16:38:56

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#234 2007-01-12 01:45:04

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#235 2007-01-12 06:26:02

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#236 2007-01-12 08:11:38

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#237 2007-01-12 16:51:48

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#238 2007-01-12 20:18:24

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#239 2007-01-13 03:11:22

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#240 2007-01-13 03:55:14

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#241 2007-01-13 03:56:54

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#242 2007-01-13 04:06:43

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#243 2007-01-14 01:07:43

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#244 2007-01-14 06:44:42

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#245 2007-01-14 08:10:18

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#246 2007-01-15 01:26:12

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#247 2007-01-15 04:13:43

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#248 2007-01-15 05:10:48

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#249 2007-01-15 09:00:59

Re: 0.9999....(recurring) = 1?

#250 2007-01-16 01:04:55

Re: 0.9999....(recurring) = 1?

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