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Quote:
" the above must = 2"? So now you're trying to prove that 0.1 = 1? In what world does "0.999... = 1" mean that "0.999... + 0.1 = 2"? No way, no how. 0.999 + 0.1 = 1.0999..., which for the same reasonings described many times about the odd nature of the repeating 9s, also = 1.1. But it certainly does not = 2, ever."
A.R.B
1 - 0.9 = 0.1 and so if 0.999... also equals 1 then 0.999... - 0.1 also = 0.1
if 1 and 0.999... are the same as you both keep saying they are?
then 1 + 0.1 = 1.1 and so does 0.999... + 0.1 = 1.1 and not 0.999... + 0.1 = 1.0999...,
Quote:
" What Ricky said. The reason that computers won't be able to answer a question such as "Why?" is that such a question makes no sense and so is unanswerable without further details of what exactly the why is about. "
A.R.B
Thank you for agreeing with me! it makes no sense concerning logical discussion!
but deep within "WHY!" there is a lot to be found! Humans have tried and some have understanding! but I'm sure Computers have no Chance!!
Quote:
" Math doesn't lie, but it can be wrong if the fomulae used don't make sense. If 1 + "infinite difference!" = 1.1, then 1.1 - 1 = "infinite difference!", therefore "infinite difference!" = 0.1
That means that by your idea 0.999... + 0.1 = 1? but we know that 0.999... + 0.1 = 1.0999... which is definitely not 1. So there's obviously a problem with your formulae. "
A.R.B
Let's make this clearer!
Quot: " but we know that 0.999... + 0.1 = 1.0999... "
A.R.B
even 1 + 0.1 = 1.1 so how can the above 0.999... + 0.1 = 1.0999...
as I have said if you think 0.999.. = 1 then the above must = 2
To Maelwys
Quot:
" but we know that 0.999... + 0.1 = 1.0999... which is definitely not 1. "
A.R.B
But wait a minute! according to the way you think! 1 + 0.9999.. must equal 2 does it not?
after all you keep saying 0.999... equals 1
To Toast!
No Matter how power full Computers get! will they ever be able to answer the ultimate Question below!
WHY!
Quote:
" From the bold text, it is then clear that "the Infinite Difference!" = 0.1, which is clearly wrong. "
A.R.B
Math don't lie! Does it!!
Quote:
" and it makes no sense to my mortal brain. "
Truth is Truth is Wonder full!...............................................................................................
To Patrick!
Imagination could help you!!
Thank you! George,Y " you a Marvel of information! "
Thanks!!
A.R.B
Quote:
" So what is 1 - 0.9999... equal to, then? "
A.R.B
1 - 0.9999... has to equal a Number <> 1 and a Number <> 0.9999...
The Magic Number is the Infinite Difference!
So that ( 1 + the Infinite Difference! ) = 1.1 and ( 0.9999...+ the Infinite Difference! ) = 1
Thank you Everyone! It is worth pointing out proofs FOR 0.999... <> 1 presented here: http://www.mathsisfun.com/forum/viewtopic.php?id=6069
All gets Confusing when a Soul is supposed to be alive forever! I imagine Animals have Souls as well!
A.R.B
1 - Infinite 0.9 = 0 is a Contradiction! because the Calculation is saying the .9's End!!
A.R.B
Thanks George,Y!
Unfortunately I never give up! even more now you have said that!
It would help if others explained things in a more clearer way! I think some people are afraid of explaining in a simple way! because they worry others may think they don't know what they are talking about! elaborate Math prevents Ideas Expanding!!
A.R.B
Lets have a look at why Infinite ( 0.9 ....0.1 ) and ( 0.99....0.01 ) etc. have the same Infinite Difference!
If we are talking about normal single Numbers! then sure 0.9 and 0.1 and 0.99 and 0.01 all have different values!
But because we are talking about Infinite Numbers! the Values are different! because the Decimal point is Infinite.
Example 1 ( 1 ) - ( 0.9 ) " Stage one/Decimal place " = 0.1
Example 2 ( 1 ) - ( 0.99 ) " Stage two/Decimal place's " = 0.01
Example 3 ( 1 ) - Infinite ( 0.9 ) " Stage Infinite/Decimal place's " = 0.001...etc.
For Example 1 above both Infinite ( 0.9 ) and the Infinite Difference ( 0.1 ) Shift one Decimal place! and so remain equally Different! they both will always have a Value!
For Example 2 above both Infinite ( 0.99 ) and the Infinite Difference ( 0.01 ) Shift two Decimal place's! and so remain equally Different! they both will always have a Value!
For Example 3 above both Infinite ( 0.9 ) Infinite Decimal place's) and the Infinite Difference
( 0.001...etc. ) Infinite Decimal place's) Shift Infinite Decimal place's! and so remain equally Different! they both will always have a Value!
Neither can ever equal Zero! because it would be a Contradiction to the Definition Infinite!
Quote: " it is a formula already "
Quote: " I think it's pretty clear what Zhylliolom said..."
A.R.B
Does the formula? show whether the 1482 different possible Maps are the Same! etc......
Does the formula show how many Regions : Common borders : Colours etc......there are!
To luca-deltodesco
Quote:
" 0.99 + 0.001 = 0.991, not 1, if you can't even get that right..."
A.R.B
The Main thing is that you understood what I meant! Strange that! everything else I put forward you don't understand! I make a mistake with a Zero! and you understand it!?
To keep everything Fare again! can all other Posts not to do with this Post! be removed again! including the Link above! to the other Post!
A.R.B
To luca-deltodesco
Quote: " 1-0.9 = 0.1 (youre 'infinate difference')
1-0.99 = 0.01 (your 'infinate difference' again)
clearly, 0.1 and 0.01 aernt the same"
A.R.B
0.9 + 0.1 = 1
0.99 + 0.01 =1
Same difference!!
To Zhylliolom
Quote: " A map on an orientable surface of genus g needs a maximum of γ colors, where γ is given by "
Could you possibly give your example using Simple Variables! ie R,B.1,2,3,4 etc. so we can look at the Math! in a way to make it Into a Formula!
To Maelwys
Quote: " Why does it have to start from somewhere? It's a number, it's not starting anywhere and it's not going anywhere... it just is. "
A.R.B
Are all your Mathematical idea's Calculations based on the above Quote: of yours!
you have to show how you arrived at a Number to represent Infinite 0.9 before you can give any arguments about it!
Not knowing where Infinite 0.9 has come from! or how it is made! is the main reason you cannot grasp anything concerning my Formula!
From my Formula again!! the Calculation C ( A/B ) x B shows the Number ie. 0.9 is being Multiplied x 1.111... etc to achieve Infinite 0.9
If A from my Formula was Multiplied x 1.111 it will also always be greater than C
A(1) Starts as a higher Value than C(0.9) and so will always be greater! ( no Algebra signs + x etc. are used to make up the difference! )
D(A-C ) will always contain the Infinite Difference missing from C.
To luca-deltodesco
The term " Infinite Difference " is just to explain that any Difference is one of the same!
we are after all talking about from the Start onwards!
To Maelwys
Quote:
" Can you explain the "Infinite Difference Remaining the Same" proof? "
A.R.B
1 - ( 0.9 ) = ( 0.1 ) " Infinite Difference " which makes 0.9 < 1
1 - ( 0.999... ) = ( 0.001... )" Infinite Difference " which makes 0.999... < 1
The length of the above two examples! makes no difference to the actual difference remaining the same!
Quote:
" Can you explain the terms "Single Start Value" and "Infinite < 1 Value"? "
A.R.B
Infinite 0.9 has to start from somewhere! 0.9 is the Start/Stage one/Decimal Place for Infinite 0.9
The Infinite < 1 Value is the Value that always remains when 1 subtracts the Infinite 0.9 Value from the Start/Stage one/Decimal Place onwards.
Quote:
"Also, explain your proof of why D <> 0? You can't simply disregard that case because you don't like the idea, you have to prove that it can't be true, or your statement that C <> C + D doesn't hold for the case where D = 0 (which it does, according to your definitions of C and A)."
A.R.B
It is impossible foe D to ever = 0 because D is made up from the Infinite Difference
D ( A - C ) where that A started as an Infinitely greater value than C because C ( A/B ) x B
is where that C is calculated by multiplying the Value 0.9 x 1.111..... etc.
the Value C that has been multiplied by 1.111..etc.. will always be less than the Value A that starts as = 1 because 1 is a whole Number with a higher Value,and C is a value that has been divided within 1 which makes it permanently < 1
To mathsyperson Moderator
Thank you for your opinion!
A.R.B
Here is an Interesting Challenge!
Is it possible to make a Formula to prove the Four Colour Theorem Problem?
The Proof as it stands was put forward by Haken & Appel ( 1976 ) using a Computer! and then double checked using an independant Computer,taking aproximately 1200 Computer hours.
The Computer found 1482 different possible Map configurations,and is accepted as a Proof! even though some Mathematicians are not happy! because it was not fully checked by Humans! the main reason being they have not found anyone or group of people ( as far as I know ) willing to check all 1482 configurations.
What makes the Challenge of finding a Formula to Prove the Four Colour Theorem,Interesting is! will the Formula agree with the Computer and produce the same total 1482 different possible Maps! if not? then it can again be looked into further.
I am interested in this myself at the moment,and if anyone else would like to put ideas forward on how it can be done! then please do.
I think using Variables would be a good idea,so as to see what is happening in the Calculations,a start area might be as with the Variables below.
R = Regions : B = Common borders : Colours could be Numbers 1,2,3,4 etc..
History:
The original Four Colour Theorem idea came from," Francis Guthrie " England ( 1852 ) and said!
" What is the minimum number of colours required,to colour any conceivable map,such that no two regions having a common border have the same colour. "
A.R.B