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To Maelwys
Can you just put one clear Question forward at a time! and make is clear! not multiple replys!
To Maelwys
Quote:"
0.555... = 0.5? But I know that 0.555... is the same as 5/9, and 0.5 is the same as 1/2, so there's a difference between them of 1/18, obviously not equal. Or, if you want to avoid fractions, I know that 0.5 < 0.54321 < 0.555..., so if there's a number between the other two numbers, how are they equal? "
A.R.B
This Math has nothing to do with Infinite Recurring Numbers!
To Maelwys
Quote:"
So if half of 0.000...1 = 0.000...5, then what is 0.000...1 * 5? When there's an infinite number of 0s before the 1, how do you add one zero to show that the 5 is actually smaller than the 1, and not bigger than it? "
A.R.B
Why are you trying to Calculate x 5 what has this to do with what you asked!
0.000...1 = 0.000...5, then what is 0.000...1 * 5?
0.1 / 2 = 0.05 so 0.05 x 2 will always be equal to 0.1 again!
To Maelwys
Quote:"
If 0.999... is 0.000...1 difference from 1, where 0.000...1 has an infinite amount of 0s, followed by(?) a 1, then what is half of the value of 0.000...1?
A.R.B
0.1 / 2 = 0.05 and another example 0.01 / 2 = 0.005 Infinite example = ( 0.001...) / 2 = ( 0.0005...)
For any two numbers that are not equal, we should be able to find the average of those two numbers, being equal to half the difference between them. So the average of 0.999... and 1 should be equal to 0.999... + (0.000...1 / 2), so I'm wondering how you believe we'd be able
to do that math, and what the answer should be?
A.R.B
0.9 / 2 = 0.45 and another example 0.99 / 2 = 0.495 Infinite example = ( 0.999...) / 2 = ( 0.4995...)
So ( 0.9 ) = ( 0.45 ) + ( 0.05 ) = 0.50
So ( 0.99 ) = ( 0.495 ) + ( 0.005 ) = 0.50
and Infinite ( 0.999...) = ( 0.4995...) + ( 0.0005...) = 0.50
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Quote: "
Also, you conveniently answered only half of post # 587, pointing out that my initial translation of it was incorrect, but then never actually answering my correct translation of it, by explaining how 0.555.... = 0.5, when there's a 0.0555... difference between them.
A.R.B
If your 0.555... is an Infinite Recurring ( 0.5 ) then as we all know the Value is Infinitely Repeating Itself! so the Value will always be the same! length makes no difference!
Infinite Recurring ( 0.5 ) = 0.5 because! ( 0.5 ) will always = 0.5
To Sekky
Quote: " start accepting basic facts about field theory "
A.R.B
I am more than sure!! the only field theory you really know about! is being in a field! with field mice!..
To Maelwys
A.R.B
remind me! it would help if you only gave one reply! but I may have to go for now!
To Sekky
A.R.B
when the apple falls on your head! you may wake up!! but untill then! take notes from someone who knows more then you!
To Maelwys
Quote: " 1.5000... = 1.4999... "
A.R.B
1.5000... - 1.4999... = 0.0001 this is an Infinite Calculation! and can be proved the same Difference exists! no matter how many decimal places you want to try!
Example A = Infinite ( 1.50 ) B = Infinite ( 1.49 ) A - B = 0.001...
To Maelwys
Quote: " I was just reading your answer the way it was written, because it's not the 0.2 that's recurring, it's just the 2, so it should be written as 0.222... = 0.(2), not (0.2). "
A.R.B
we are only talking about Infinite Recurring ( 0.2 ) the 0.2 Value is endless! so must always have the same Value!
To Sekky
Quote: " ...so give them both different names, they'll still be the same value
call them "stupid" and "moron", accept that they have the same numerical value, and how you write them in text doesn't make a blind bit of different to how you use them in practise. "
A.R.B
so just SHUT you up in one big swoop!
you will find! they must both equal! Infinite Recurring ( n ) = n because! ( n ) will always = n
To Sekky
Quot:
" They are the same value, with two real value decimal expansions. "
A.R.B
can you give us the same value? with two real value decimal expansions.?
To Maelwys
Quote: " Wow, that's so wrong.... So 0.222... = 2? "
A.R.B
How is it!! everything you read!? you dont understand!!
Infinite Recurring ( 0.2 ) = 0.2 because! (0.2 ) will always = 0.2
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THE INFINITE/RECURRING ( N ) = N PROOF 11/03/07 by Anthony.R.Brown
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Infinite Recurring ( n ) = n because! ( n ) will always = n
To Sekky
Quote:
" Wrong, any terminating rational expression has two real valued decimal expansions "
A.R.B
an expression! such as INFINITE/RECURRING 0.9 can only have one Value! if there were
" two real valued decimal expansions ? " then there would be a Contradiction!!
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THE DEFINITIVE REASON INFINITE/RECURRING 0.9 IS < 1 AND <> 1 10/03/07
by Anthony.R.Brown
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( 1 ) If any Number Starts or has a Zero followed by a Decimal point at the beginning! it will always be < 1 and <> 1 if no additional Math is applied to the Number!
( 2 ) Numbers that conform to ( 1 ) as examples are 0.1 to 0.9
( 3 ) Infinite/Recurring Numbers have no end! the Numbers repeat themselves endlessly!
( 4 ) Because Infinite/Recurring Numbers are always the same Number being repeated,we don't need to try and write down many as examples,because the Number is always the same.
( 5 ) An example for ( 4 ) is Infinite/Recurring ( 0.9 ) = 0.9 the reason this is True is because the Number never changes!
( 6 ) The same can be applied to any Infinite/Recurring ( N ) = N
( 7 ) From ( 5 ) and ( 6 ) we can prove Infinite/Recurring ( 0. 1 ) to ( 0.9 ) < 1 and <> 1
1 - ( 0.1 ) = 0.9 and <> 1
1 - ( 0.2 ) = 0.8 and <> 1
1 - ( 0.3 ) = 0.7 and <> 1
1 - ( 0.4 ) = 0.6 and <> 1
1 - ( 0.5 ) = 0.5 and <> 1
1 - ( 0.6 ) = 0.4 and <> 1
1 - ( 0.7 ) = 0.3 and <> 1
1 - ( 0.8 ) = 0.2 and <> 1
1 - ( 0.9 ) = 0.1 and <> 1
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To Maelwys
Quote:
" Does it matter where these numbers "come from"? "
A.R.B
This is your Main Problem! as I said many times! Infinite/Recurring Numbers are not Plucked from the Sky!
you have to show the Math on how the Infinite/Recurring Numbers are made! so far you think they have no Start!
If you can show any Infinite/Recurring Number without a Start! you will be a Genius!!
To Maelwys
Quote:
(1) " This proof has been countered many times, and you've still yet to raise a coherant defense for it. "
(2) " This quote has also been rebuttled above. "
(3) " I don't even understand this one... there's a 10% difference between what? 0 and 9? And where did the 1.8, 2.7, etc, come from? I'm thoroughly confused, sorry. "
A.R.B
you are joking of course!
(1) C <> ( C + D ) " INFINITE 0.9 <> 1 " " C must always = .999... and D must always = .001...
(C + D ) or A only = 1 " That's an Infinite Proof!! " making C < 1
........................................................................................................................................
(2) Prove yourself wrong with this one! and give us your Definition for Recurring?
(3) you will always be " thoroughly confused " unless you learn where Numbers come from! and how they are made!
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INFINITE 0.9 <> 1 PROOF : FORMULA : By,Anthony.R.Brown,12/02/07
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A = 1 " Single Start Value For 1 "
B = 0.9 " Single Start Value For 0.9 "
C ( A/B ) x B " Infinite 0.9 Value "
D ( A - C ) " Infinite < 1 Value "
C <> ( C + D ) " INFINITE 0.9 <> 1 "
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RECURRING DEFINITION PROOF 03/03/07 by Anthony.R.Brown.
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The Definition for Recurring is given below..............................................................................
A Number that repeats itself Endlessly! Continuously repeating the same Number!
Below are examples of Recurring Numbers! They are of course Endless! Length is example only!
Recurring ( 0.1 ) = .111111111111111111111111111111111111111111111111111111111111111
Recurring ( 0.2 ) = .222222222222222222222222222222222222222222222222222222222222222
Recurring ( 0.3 ) = .333333333333333333333333333333333333333333333333333333333333333
Recurring ( 0.4 ) = .444444444444444444444444444444444444444444444444444444444444444
Recurring ( 0.5 ) = .555555555555555555555555555555555555555555555555555555555555555
Recurring ( 0.6 ) = .666666666666666666666666666666666666666666666666666666666666666
Recurring ( 0.7 ) = .777777777777777777777777777777777777777777777777777777777777777
Recurring ( 0.8 ) = .888888888888888888888888888888888888888888888888888888888888888
Recurring ( 0.9 ) = .999999999999999999999999999999999999999999999999999999999999999
The above examples are shown to be True! in the Calculations below! According to the Definition for Recurring!
( 0.1 ) Recurring < 1 and <> 1
( 0.2 ) Recurring < 1 and <> 1
( 0.3 ) Recurring < 1 and <> 1
( 0.4 ) Recurring < 1 and <> 1
( 0.5 ) Recurring < 1 and <> 1
( 0.6 ) Recurring < 1 and <> 1
( 0.7 ) Recurring < 1 and <> 1
( 0.8 ) Recurring < 1 and <> 1
( 0.9 ) Recurring < 1 and <> 1
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INFINITE 0.9 <> 1 PROOF : THE INFINITE 10 % PERCENT DIFFERENCE 03/03/07
by Anthony.R.Brown.
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One of the most Accurate and sound ways to prove Infinite 0.9 <> 1 is to give the Infinite Percent Difference Values from the Start Onwards!
The example below is for the first Ten Decimal Place's,which clearly shows the count increasing as more and more Infinite .9's are looked at! But remain a constant Difference of 10% in relation to how far the example has traveled.
Count = ...... ( 1 ).....( 2 )....( 3 )...( 4 )....( 5 )...( 6 )....( 7 )....( 8 )....( 9 ).....( 10 )
Infinite 10 %
Difference =..(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%)...(10%)
Infinite 0.9 = ( 0.9 ) ( 1.8 ) ( 2.7 ) ( 3.6 ) ( 4.5 ) ( 5.4 ) ( 6.3 ) ( 7.2 ) ( 8.1 ) ( 9 )
................... ( x 1 ) ( x 2 ) ( x 3 ) ( x 4 ) ( x 5 ) ( x 6 ) ( x 7 ) ( x 8 ) ( x 9 ) ( x 10 )
Infinite 0.9 Onwards! there will always be a 10 % Difference making it Impossible for Infinite 0.9 to ever = 1
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p.s This is my last Post on this so called Math forum! unless the Post title is Changed to something that is not BIASED!
The Moderators! and Admin should only be Referees! and not have any Personnel Opinions on the Math subjects! and especially not allow titles like this! that straight from the Start are clearly expressing a BIASED View!
Bye from A.R.B ..................................................................................................................
To George,Y
(:
Another reason!
a lot of Questions! have been resolved on the other one! let's start a fresh!...............................
A.R.B
To Sekky
Quote:
" In a word, no.
If you really care why I'll find some resources. "
A.R.B
where can you remember the Word NO! from!!
To Maelwys
Quote:
" Isn't this just ANOTHER duplicate topic of the conversation that's already gone on at 4 different threads by now? Can't we just keep it all in one place? "
A.R.B
The Post heading is Unbiased!
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INFINITE 0.9 <> 1 PROOF : FORMULA : By,Anthony.R.Brown,12/02/07
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A = 1 " Single Start Value For 1 "
B = 0.9 " Single Start Value For 0.9 "
C ( A/B ) x B " Infinite 0.9 Value "
D ( A - C ) " Infinite < 1 Value "
C <> ( C + D ) " INFINITE 0.9 <> 1 "
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RECURRING DEFINITION PROOF 03/03/07 by Anthony.R.Brown.
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The Definition for Recurring is given below..............................................................................
A Number that repeats itself Endlessly! Continuously repeating the same Number!
Below are examples of Recurring Numbers! They are of course Endless! Length is example only!
Recurring ( 0.1 ) = .111111111111111111111111111111111111111111111111111111111111111
Recurring ( 0.2 ) = .222222222222222222222222222222222222222222222222222222222222222
Recurring ( 0.3 ) = .333333333333333333333333333333333333333333333333333333333333333
Recurring ( 0.4 ) = .444444444444444444444444444444444444444444444444444444444444444
Recurring ( 0.5 ) = .555555555555555555555555555555555555555555555555555555555555555
Recurring ( 0.6 ) = .666666666666666666666666666666666666666666666666666666666666666
Recurring ( 0.7 ) = .777777777777777777777777777777777777777777777777777777777777777
Recurring ( 0.8 ) = .888888888888888888888888888888888888888888888888888888888888888
Recurring ( 0.9 ) = .999999999999999999999999999999999999999999999999999999999999999
The above examples are shown to be True! in the Calculations below! According to the Definition for Recurring!
( 0.1 ) Recurring < 1 and <> 1
( 0.2 ) Recurring < 1 and <> 1
( 0.3 ) Recurring < 1 and <> 1
( 0.4 ) Recurring < 1 and <> 1
( 0.5 ) Recurring < 1 and <> 1
( 0.6 ) Recurring < 1 and <> 1
( 0.7 ) Recurring < 1 and <> 1
( 0.8 ) Recurring < 1 and <> 1
( 0.9 ) Recurring < 1 and <> 1
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INFINITE 0.9 <> 1 PROOF : THE INFINITE 10 % PERCENT DIFFERENCE 03/03/07
by Anthony.R.Brown.
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One of the most Accurate and sound ways to prove Infinite 0.9 <> 1 is to give the Infinite Percent Difference Values from the Start Onwards!
The example below is for the first Ten Decimal Place's,which clearly shows the count increasing as more and more Infinite .9's are looked at! But remain a constant Difference of 10% in relation to how far the example has traveled.
Count = ...... ( 1 ).....( 2 )....( 3 )...( 4 )....( 5 )...( 6 )....( 7 )....( 8 )....( 9 ).....( 10 )
Infinite 10 %
Difference =..(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%)...(10%)
Infinite 0.9 = ( 0.9 ) ( 1.8 ) ( 2.7 ) ( 3.6 ) ( 4.5 ) ( 5.4 ) ( 6.3 ) ( 7.2 ) ( 8.1 ) ( 9 )
................... ( x 1 ) ( x 2 ) ( x 3 ) ( x 4 ) ( x 5 ) ( x 6 ) ( x 7 ) ( x 8 ) ( x 9 ) ( x 10 )
Infinite 0.9 Onwards! there will always be a 10 % Difference making it Impossible for Infinite 0.9 to ever = 1
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manner. Moderator action has been taken against those who are not civilized by Ricky and Zach. ]
The above obviously means nothing! has no Values! no standards! and no morals!
A.R.B
To Maelwys
Quote:
" Those aren't infinite numbers, those are real numbers (you're just multiplying 0.9 x 1.1, no infinite-long recursions involved in that). You can't apply normal rules for finite numbers into infinitely recursive "
A.R.B
How many times do I have to explain it to you! they are the start! unless you can show how Infinite Numbers start in a Different way! then you have no argument!!