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My Theory is that there is an Infinite Dimensional Solution to Space and Time!
A.R.B
Does God!? Come before the Chicken or the Egg! or Both!
I have always felt it is more than Coincidence! That God is Dog backwards! Just as the Egyptians knew Dogs are our protectors! And had them standing outside Sacred Tombs within Pyramids!
A.R.B
To Ricky!
the above is not a Quote: of mine! only Info!
Does anyone know if pi has more Even! or more Odd! Numbers,or is it the same % Calculated so far!
Plus! the Zero's
A.R.B
More Info!
A paradox is an apparently sound statement or proposition which leads to a logically unacceptable conclusion. One such statement, known as the barber's paradox, goes thus:
In a village there is a barber. The barber cuts the hair of everybody in the village who doesn't cut their own hair. In other words: If someone cuts their own hair then the barber doesn't cut their hair. If the barber cuts their hair then they don't cut their own hair.
The paradox arrises when you consider who cuts the barbers hair. If the barber cuts his own hair then the barber doesn't cut his hair. If the barber doesn't cut his own hair then then the barber cuts it.
Russell's paradox, named after its discoverer Bertrand Russell, is a mathematical paradox based on set theory. Consider a set called S which is the set of sets that do not contain themselves. If S is not an element of S, then by definition it must be an element of S. If S is an element of S then it cannot be an element of S.
n.b. the following does not display correctly in Microsoft Internet Explorer (the boxes should show the "not an element of" symbol):
S[x | x ∉ x]
S ∈ S → S ∉ S
S ∉ S → S ∈ S
This effectively means that true = false and false = true. This could be of great usefulness in maths exams because it means that if you can prove that you have got a question wrong then you can also mathematicaly prove that it is also correct.
I have an Idea pi is a Circle! and eventually the two ends of the Circle will meet!
and when they do? the True Value for pi would have been found!
Maybe after some enormous Calculation the end joins the Start again!
Another interesting point is! if the Barber had never Shaved once! ( Male or Female ) and just let their Beard grow! they could in fact Shave themselves! once! because they would have no History of being a person that Shaved themselves!
Good Advert! egeniius!
have you found a Pattern!
A.R.B
The problem with some of this is! that some woman! do have Beards! I can only imagine they do sometimes shave!
My answer was only to Split the task into two! which is half doing and half not! I think the Original " Barber's Paradox! " should have had a Clause! about Others! ie Woman!
I have a very Interesting Idea!
is it possible to convert pi to Computer code! represented by 1's and 0's
this may help to find a pattern!?
The Original " Barber's Paradox! " is a Question involving a 50% Contradiction!
So I,m giving an Answer! that satisfies Both Situations! 50%
an unequal answer! for an unequal Question!
Suppose you walk past a barber's shop one day, and see a sign that says
"Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else."
This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself? If he does, then he mustn't, because he doesn't shave men who shave themselves, but then he doesn't, so he must, because he shaves every man who doesn't shave himself... and so on. Both possibilities lead to a contradiction.
A.R.B
The Barbers Wife shaves the Barber!! the first time! and then every other time! after the Barber has shaved himself once! in a row Only!!
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FOUR COLOUR PROBLEM FORMULA : BREAKTHROUGH! 16/03/07 By Anthony.R.Brown
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The way to tackle this problem is based on the 1482 possible maps! Found by the Computer.
I looked at the way the Numbers 1 to 10 divide into the Magic Number 1482
1482 / 1 = 1482 *
1482 / 2 = 741 *
1482 / 3 = 494 *
1482 / 4 = 370.5
1482 / 5 = 296.4
1482 / 6 = 247 *
1482 / 7 = 211.71428
1482 / 8 = 185.25
1482 / 9 = 164.666...
1482 / 10 = 148.2
4 COLOURS:
I noticed from the above Calculations that only four Numbers divide into 1482 marked * with no amount left over!
Could this be the Calculation that says we need Four Colours for any Map!
6 MAIN POINTS:
From the above Calculations 1482 / 6 = 247 on any Map that requires the Four Colours,there are 6 main points.
3 POINTS AT EVERY MAIN POINT:
From the above Calculations 1482 / 3 = 494 on any Map that requires the Four Colours,there are 3 points that meet at every one of the 6 main points.
9 BORDERS:
From the above Calculations 1482 the 6 = 247 main points + the 3 = 494 points at every main point make up the connections for the 9 Borders on any Map that requires the Four Colours.
The above observations are a starting point! In trying to put together a Formula for this marvellous problem!
The more contributions put forward by everyone! The better! It's there for the taking,it could make this Math forum famous!
A.R.B
To Maelwys
First of all Congratulations! With your persistence's in trying to understand the problems! Associated with Infinite/Recurring 0.9 Everyone will all Benefit from it!
I have not been able to explain fully! What I'm trying to say, because we have only been concentrating on Infinite/Recurring 0.9 as if it is unique in the world of Infinite/Recurring Number/Values.
I have always known this not to be true! All Infinite/Recurring Number/Values behave in the same way according to the type!! They belong to,there are Normal Number/Values and Infinite/Recurring Number/Values and Infinite/Recurring Difference Number/Values.
Example Normal 0.1 = 0.1
Example Infinite/Recurring 0.1 = 0.111...
Example Infinite/Recurring Difference 0.1 = 0.001...
With the three examples above! They can all equal the Value 1
Normal 0.1 + Normal 0.9 = ( 0.1 + 0.9 ) = 1
Infinite/Recurring 0.1 + Infinite/Recurring 0.9 = ( 0.111... + 0.999... ) = 1
With the second example above! Because the 0.1 and 0.9 are Infinite/Recurring the same Start Values are being repeated over and over again!and actually equal ( 0.1 + 0.9 ) and not ( 0.111... + 0.999... ) as if the Values are getting larger which of course would be 1.111...etc.
Infinite/Recurring Difference 0.1 + Infinite/Recurring 0.9 = ( 0.001... + 0.999... ) = 1
With the third example above! Because the 0.1 is the Infinite/Recurring Difference we Know that the Value has come from ( 1 - Infinite/Recurring 0.9 ) there will always be a .1 Difference the .00 is the Decimal Point Shift!
The above Shows how there can be Three Different Types of 0.1 and why its Important to know which one is being used in any Calculations!
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To Maelwys Examples for 0.8
Again you are Comparing Normal Number Calculations with Infinite/Recurring Number Values!
8 / 10 = 0.8
8 / 9 = 0.888...
For 0.9 The Normal Calculations above give Different Results! And also for some other 0.1 to 0.9 Values!
9 / 12 = 0.75
9 / 11 = 0.8181818...
9 / 10 = 0.9
9 / 9 = 1
9 / 8 = 1.125
So the above shows using the Same Normal Calculations! There is no Infinite/Recurring 0.9
What we need is a more Precise way for Calculating Any Infinite/Recurring Number Values!
The best way I know is Multiplying the Original Start Value! By Infinite 1.111...
This will then give a True Infinite/Recurring Number Value! For Any 0.1 to 0.9 Value.
Now going back to your original question how can 8 / 10 be equal to 8 / 9 the Answer is they are not! Concerning Normal Number Calculations! Even though they both have a 0.8
Firstly the 0.8 for 8 / 10 is 0.8 and not the Start! For 8 / 9 it does have a 0.8 at the Start! But as I have pointed out,it is not possible with some other 0.1 to 0.9 Infinite/Recurring Number Values!
Calculated in the way you have put forward!
To Maelwys
A.R.B
as I said I will have to go for now! I will answer! 14/03
To
luca-deltodesco
I doubt if WE! could with you!
To
luca-deltodesco
Quote: " anthony, what is your first language (please say its not english) "
A.R.B
I'm good at Sign language! wish I could show you!
To Maelwys
Quote:
"So, instead we'll deal with 0.888... as I understand what you're saying, when I look at 0.888... I'm actually looking at 0.8? And the difference between 1 and 0.888... is 0.2? Is that right?"
A.R.B agreed! let's look at the above! p.s I will only be online for the next 45 minutes! incase I cut off the conversation!
To Maelwys
Quote: "
So where does the 1 go in the second number? If the 0s are infinite/recurring, always the same, with no after, then there's nowhere to put the 1. "
A.R.B
The 1 does not go anywhere!
with 0.9999..... even though we can see many .9's we are in fact always looking at one .9
with 0.0001..... even though we can see many .0's we are in fact always looking at one .1
because .1 is the actual Infinite Difference! from the Start!
There has to be a Value between 0.9 and 0.1 and that is 0.000...the Decimal Shift!
The Infinite Difference does not Grow! is stays the same and is shifted!
To Maelwys
Quote: "
What about 0.909090909090909090....? How do you represent that as starting as one decimal place? "
A.R.B
Ok for 0.909090909090909090....? " The starting decimal place! is the when the number changes in sequence! for the above it starts as 0.90
Quote: "
0.9999999999999999999999999999999999999999999999999999999999999999999999..........
0.0000000000000000000000000000000000000000000000000000000000000000000001..........
What comes after the ... in this example? "
A.R.B
It is always the Same! there is no after! the... as far as we can Calculate and show there will always be .999... and .001... both must be Infinite/Recurring!!
To Maelwys
Where you are making mistakes! is you are trying to Calculate Infinite/Recurring Numbers/Values! as if they are Normal Numbers/Values!
If you really do believe Infinite/Recurring 0.9 never ends! then it must also be True for Any Infinite/Recurring Numbers/Values! what is True for one,must be True for all others!
The other thing you must accept is that all Numbers/Values have a Start!
Infinite/Recurring 0.9 " Starts as one Decimal place! "
Infinite/Recurring 0.1 " Starts as one Decimal place! "
Infinite/Recurring 0.1 + Infinite/Recurring 0.9 " Starts as one Decimal place! " and so from the Start onwards must always = 1
The two examples below will always run along side each other! as an Infinite Difference!
0.9999999999999999999999999999999999999999999999999999999999999999999999..........
0.0000000000000000000000000000000000000000000000000000000000000000000001..........
To Sekky
Quote:
" You are a child, good look getting a seat at any academic establishment with that attitude. "
A.R.B
Is the above ENGLISH!!
To Maelwys
Quote:
"
What do you mean "the calculation infinitely repeats itself"? Why can't I multiple the number 0.000...1? You told me that 0.000...1 / 2 = 0.000...5 up above, so if I can divide it "
A.R.B
Mainly because none of this has anything to do with Infinite Recurring Numbers!
my examples showed you from the start onwards! because we cant look at the end!!
Infinite Recurring ( n ) = n because! ( n ) will always = n
The above will always be true!
To Maelwys
Quote:
"But its not 0.0001 or 0.00000001, it's 0.000...1 with an infinite number of 0s. The ... doesn't refer to an unknown number of digits, it refers to an infinite number of digits. So what is it then?"
A.R.B
Infinite Recurring ( 0.1 ) x 5 = Infinite Recurring ( 0.1 ) Because the Calculation Infinitely Repeats Itself!!
To Maelwys
Quote:
" I'm trying to compare two numbers. What is 0.000...1 * 5? "
A.R.B
0.000...1 * 5 " If this is 0.0001 x 5 then = 0.0005 If this is 0.0000001 x 5 then = 0.0000005