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Is there a Condition! Known as SLIDE-RULE-NISM Where someone Loves! Slide Rules!........
A.R.B
Infinite/Recurring Number/Values!
Depending on how Many Decimal Places are Calculated! The Static Value Changes!
Infinite/Recurring 0.9 ( One Decimal Place ) 0.9 has a Different Static Value To ........................
Infinite/Recurring 0.9 ( Two Decimal Place's ) 0.99 ...............................................................
Everyone Knows Cars have Manifolds!!
To luca-deltodesco
Quote:" find then, there is no such thing as a number/value that has a non static-value, otherwise its a variable, not a number/value "
A.R.B
Next you will be Saying Infinite/Recurring Number/Values are Integer Whole Number/Values!
To luca-deltodesco
Quote:" there is no such thing as a number that has a non static-value, otherwise its a variable, not a number "
A.R.B
I Said Number/Value! " Knowing we are Talking about Infinity! is the point! "
To Maelwys
Quot:" So your argument is that 0.999... isn't a real number, then? Like I said above, this argument at least might have half a leg to stand on. "
A.R.B
Infinte/Recurring 0.9 is a Number/Value But not a Fixed Number/Value! as with Whole Numbers!
Infinite/Recurring 0.9 = 0.(n) < 1 The 0.(n) is the Value from 1 - Infinite/Recurring 0.9 = 0.001...
So we can have 0.999... and 0.001... Where 0.999... + 0.001... = 1
To Maelwys
Quote:" But what number is halfway between "Infinite 0.9 (Stage Infinite Decimal Place's)" and 1? "
A.R.B
There is no Halfway! Concerning Infinity! But from Infinite/Recurring 0.9 ( Stage 0ne Decimal Place ) There will always be More 0.9's
To Maelwys!
At Last we Agree on Something!...........................................................................................
Infinite 0.9 ( Stage One Decimal Place ) = 0.9
Infinite 0.9 ( Stage One Decimal Place ) + ( The Next Decimal Place " More 0.9's ) = 0.99
Infinite 0.9 ( Stage Infinite Decimal Place's ) = " More 0.9's " As always Before 1
To Maelwys
Quote:" You still never answered my above question about the average of 0.999... and 1. If 0.999... is a real number < 1, then there must be another real number existing (x) where 0.999... < x < 1. The easiest such x to find should be simply the average of the two numbers that it's between. So what is that average? What is that number that exists between 0.999... and 1? "
A.R.B
There is only More 0.9's Between Infinite/Recurring 0.9 and 1
All you have to accept! is that there are Numbers Infinitely < 1
To Maelwys
Quote:" 0.999... / 2 = 0.5, because 0.999... = 1. ;-)
Or if you prefer
0.999... / 2 = 0.4999... (which incidentally, also = 0.5) "
A.R.B
Wrong!!
0.9 / 2 " 1 Decimal Place " = 0.45
0.99 / 2 " 2 Decimal Place " = 0.495
0.9 Infinite Decimal Places / 2 " True Value can never be Calculated! "
0.4999... <> 0.5
To Ben
Quote:" But you seem not to understand that what you you call "apples" (2-sphere) and "doughnuts" (2-torus) are classic examples of 2-manifolds.
A.R.B
Some Doughnuts can be the Same Round Shape as an Apple!!
1 / 2 = 0.5
Infinite/Recurring 0.9 / 2 = ?
Now for the the Wise Guys!
give us a Math Value (Decimal Places) for 1 and Infinite/Recurring 0.9
A.R.B
I Fully Understand the Problem!
But in a Sarcastic way I'm showing How Math Simplified Examples! can make the Situation Worse! by Giving Examples Using Items like Rubber Bands! Apples! Doughnuts!
Far Better from the Start to Give actual Examples! and Simplified Math to explain the Problem!
A.R.B
So Back to the Impossible Question!
If you can Show how to Average an Unknown Number/Value Concerning Length and/or Decimal Places!
Its no Good just saying The average of Something is! "As far as Math goes! we need to know the Value as in Decimal Places! "
Otherwise we can of Course Average anything no Math needed!
Example! Average Elephant and Elephant = Elephant
Now for the the Wise Guys!
give us a Math Value (Decimal Places) for 1 and Infinite/Recurring 0.9
A.R.B
1 / 0.3 = 0.333...
1 / 0.33 = 0.030...
And not 0.3 is the same as 0.3000....,
Quote:" That's like if you said that 2 + 2 = 4 because I have 2 apples and you give me 2 apples
Have and Gave is the Start of the Problem ( 2 + 2 = 4 )
If you can Show how to Average an Unknown Number/Value Concerning Length and/or Decimal Places!
So How long/Decimal Places does 0.333... have ?
Because 0.3 is one Decimal Place!
To Maelwys
Quote:" That's like if you said that 2 + 2 = 4 because I have 2 apples and you give me 2 apples, I'll have 4 apples. And then I could counter that by saying "No, 2 + 2 = 3, because one of those apples probably has a worm in it and then I'll just have to throw it out anyway, so it doesn't really count". You can only take an example to a certain point in math. ;-) "
A.R.B
The Apples can have a Million worms! and you can throw away as many Apples as you want! Nothing will change the fact! that from the Start you had 4 Apples!!....................................
To Maelwys
Quote:" Alright, if you'll stick by your cop-out answer, that's fine for now. But it still doesn't answer:
4/ What is the average of 1 and 0.999...? "
A.R.B
If you can Show how to Average an Unknown Number/Value Concerning Length and/or Decimal Places! then you will be a Genius!! and Far better than any Math person Ever!
To Maelwys
A.R.B
Do you never Notice who the Posts are Addressed to.........................................................
To Ricky
Quote:" Anthony, I honestly thought you were just making a joke. A rather funny joke in my opinion.
But you misunderstand the problem. They use "apple" and "donut" as analogies, to give those who don't have enough mathematical knowledge a fighting chance to understand the problem. They don't actually mean a donut and apple. "
A.R.B
The fact that I have taken the Apple and the Doughnut as the Problem example! is no more foolish or Stupid than the original Statement below to Describe the Problem using of all things Rubber Bands?? (Thats also not Math? )
Poincaré Conjecture
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If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.
To Maelwys
Quote:" You're avoiding my question again. For the moment I'm not arguing that 1 and 0.999... do or don't equal each other. I'm just asking, based on your understand that 0.999... < 1, what is the result of 1 / 0.999...
It should be a fairly straightforward question, no? "
A.R.B
To be able to Divide a Number/Value into another Number/Value we have to know how long! or how many Decimal points both Number/Values have!
Example 1/0.9 = 1.111... Because 0.9 is only one decimal place! (going back to my original point about only being able to solve the Infinite/Recurring 0.9 Problem from the Sart! ) we can find the True calculation Answer!
In the case of trying to Calculate 1/Infinite 0.9 there is no way of knowing how many Decimal places long! Infinite 0.9 is! but because it is an Infinite repetition of the Start Value! we know that however long Infinite 0.9 is! it must always be < 1 the actual Value can't be wrote down! just given as 0.(n) < 1
To Maelwys
A.R.B
You need to read Post #4