# 1=0.999... infinities and box of chocolates..Phliosophy of Math...

Discussion in 'General Philosophy' started by Quantum Quack, Nov 2, 2013.

1. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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My method is general - not limited to fraction equal to unity, which seems to be your assumption. I showed how to find the fraction equal to any rational number, not greater than unity, that has a repeating decimal, using the repeat length, I'll now call: "L."

In post 397, a part of post 301, I applied my procedure to a unity fraction as that is the subject of the thread, but in post 301 I also applied it to the Repeating Decimal RD = 0.123123123123... which has L = 3. In that case my general method for finding the (now called RF, for Rational Fraction) is RF = RD = abc / 999 as L=3 with a=1, b=2 & c =3. Thus by the "green result" of 397 (or 301) We have RF = 123 / 999 = 41 / 333, which certainly is not a unity fraction.

PS I'm not sure I understood your point, if you had one, other than the one I replied too.

Again I note that the burden of proof, is extraordinary, and on those trying to tell why my method, FAILS in the special case of L = 1 with a =9 I.e. why 9/9 = 1 is not 0.999... when works in an infinite number of other cases for finding the RF equal to ANY repeating decimal, RD, not greater than unity.

3. ### Quantum QuackLife's a tease...Valued Senior Member

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Thanks Rpenner and yes the PHD Guy [it was a first pick on a Yahoo answers board so citation is useless] said more or less the same thing by identifying the 1/infinity as 1/undefined. [Which as you have stated is not the same thing as 1/infinity= 0. When infinity is considered as "undefined" it begs a serous concern when posters such as Tach refer to 1/infinity=0 as being commonly used in calculus text books. [ which is rather disappointing if true ]

Thanks again for tolerating my slow garnering of insight into what mathematics and science generally conceive of that which is infinite or infinitesimal. Your effort is greatly appreciated and I hope others reading this thread can also consider your words with out prejudice. and other "expert " posters take note that posting incorrect assessments under the banner of "authority" can be incredibly damaging to proper discussion and future learning.
[I already accept that what I have written above is "not quite right " either... but need time to consider the implications]

The reason I said that 0.999...= 1 is a "no brainer" is one puts it in the right perspective is that, if we start with the understanding of how infinity is treated then of course 0.999...=1 but only if we deal with specific and correct terms and conventions.

5. ### Quantum QuackLife's a tease...Valued Senior Member

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23,326
Another more philosophical approach to this issue is to ask:
Is the sum of what something is, what something equals to.
By this I mean:
If we draw a circle that is exactly 1 unit in diameter
and note that when we fill it with an infinite series of nines [ as in 0.999...] that all possible values with in that circle have been taken up then is it reasonable to state that 1 = 0.999... or is it better to state that 0.999... leads to the sum of 1 or that 0.999... is what makes 1, to be 1.
This is not a mathematical question but a philosophical one.

If a house is built with an infinite number of bricks is it a single house  or an infinite number of bricks?

Is it merely a matter of perspective that determines the identity?

7. 1 not = 0.999...... & 0 not = 0.111.....

rational finite( 1 ) does not equal irrational infinite( 0.999 ).....

Space = macro-micro infinite
..micro = >IN<--subdividing space INward--multiplication-by-division

0 = non-counting number

0 representative of macro-micro infinite non-occupied space beyond our finite occupied space

0 = empty column on abacus

0.111....does not equal zero( 0 )

0.999....does not equal one( 1 )

Inifinity is irrational concept except in relationship to infinite space.

Space
..1a) non-occupied and macro-micro infinite, embraces;
..1b) occupied space...

Mathematics represent values associated with;

1) finite occupied space,

2) infinite non-occupied space,

3) imaginary concepts of mind, that may not directly correlate to either of the latter 2 and 1 above.

Rational does not equal irrational.

Irrational is expressed using numerical symbols similar to rational expressed using numerical symbols.

The irrationally infinite, macro-micro infinite non-occuped space, that embraces our finite Universe of occupied space may be the only exception to our mathematical rules as correlated to involving whether an infinite value exists. Who values the irrelevant non-occupied space that exists beyond our finite occupied space Universe?

The non-occupied space exists purely as a infinite reference set of non-value/non-point(s) ha ha....

Fuller believed in the possibility of micro infinite subdivision of our finite Universe i.e. eternal increase of quanta via micro-infinite multiplicaiton-by-division of our finite Universe of occupied space.

r6

8. ### hansdaValued Senior Member

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2,424
MD, be practical, be realistic. Consider a real circular pie and you want to divide this real pie to three real people equally. In this case you have to divide the pie in a real manner and you cannot divide the pie mathematically, with a pen and paper or in a computer/calculator.

If you have to divide the pie physically in a realistic manner, you have to divide the pie geometrically. I have already explained that a pie can be divided in three equal parts geometrically.

9. ### Motor DaddyValued Senior Member

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5,425
Sure, you can divide a whole pie into 3 pieces, but what percent of the pie is each piece, and do the 3 percentages add to 100%?

I assume you are going to try to make equal pieces as we are discussing. If that is the case then do you plan to say that each piece is 33.333...% of the whole? If yes, then you have 3 pieces of 33.333...%, which is NOT the entire pie, because the entire pie is 100%, not 99.999...%! Now what? How do you explain the FACT that 3 parts of 33.333...% don't total the whole pie??? If the total of the 3 pieces doesn't total 100% then there is a piece missing! That means there are really 4 pieces! Where is the other piece? Did you feed it to Tach's dog?

10. ### someguy1Registered Senior Member

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Really? Three parts equal in area? Easy. Three congruent parts, meaning each transformable into the others via rigid motions of the plane? Extremely difficult, probably impossible. What are you going to do with the center point?

In geometry we like congruence. You would never say a circle is geometrically the same as a square, even though a circle of area 1 can be continuously transformed into a square of area 1. Why then would mere area be sufficient to geometrically divide a circular disk?

11. You promised to stop posting this nonsense if I showed you the solution to the 8-th grade geometry exercise, I showed it to you, why do you persist?

12. ### someguy1Registered Senior Member

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727
Tach, I challenged you to produce a pairwise congruent decomposition of the unit disc into three parts, and you fell back on your measure theory argument. Of course I have agreed numerous times that you have indeed partitioned the disc into three pieces that have equal measure. As I said in this thread, that's a very easy problem.

But that's like saying that geometrically, a square of area 1 and a circle of area 1 can be continuously transformed into each other, hence they are the same. It's true that they are the same in terms of area, and even under continuous transformation. But that's a very weak form of geometric equivalence.

In the 20th century, we learned that geometry is the study of groups of transformations and what they leave invariant. Read up on the work of Sophus Lie and Felix Klein.

Transformations that preserve measure are much weaker than transformations that preserve distance. This is not a controversial statement. Your disk trisection is an example. It preserves measure. But it does not preserve distances, because your extra point has to be assigned to one of the three slices; and it can't then be mapped isometrically (distance preserving) to either of the other pieces.

You seem like a reasonably smart and serious guy. I don't understand your refusal to acknowledge the point I'm making. You can't subdivide a disk into three congruent parts. Congruence by definition preserves distances. The center point simply can't be assigned to one of the pieces and still have that piece map isometrically to another piece. That's a simple mathematical fact. I really don't understand why you are following me around attacking me for my statement of a totally true mathematical fact.

Are you a sincere physics person who actually and genuinely doesn't understand what i'm saying? That when I say "groups of transformations" that you have no idea what I'm talking about? That perhaps you've never considered the difference between a measure preserving transformation and a distance preserving one? Or are you just deliberately stalking and trolling me by pretending to not understand?

13. Excellent, then you can stop trolling now.

Excellent, then you can stop trolling now.

Yes, I am . I also have an MS in Applied Mathematics, this is why I find your hair splitting so distasteful.

14. ### Motor DaddyValued Senior Member

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Just goes to show that a guy can have an MS in Applied Mathematics and still can't tell the difference between a piece and a hole.

...(wait, did I spell that right?)

15. ### LaymanTotally Internally ReflectedValued Senior Member

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1,001
Another example of this I came across recently was the base of the natural logarithm e acts in this way like Pi does.

Then, Landauer's Principle states that information can only transmit at, kT ln 2, where k is the Boltzmann Constant, and T is temperature. Then this is the amount of temperature increase one would expect to see lost from a transfer of information that came from trying to understand Maxwell's Demon. Then it would seem that it would be significant to losses of energy even though it too is an infinite number, but it also has a exact value that can be worked. Then they are finding that Landauer's Principle actually may be true, and I think there is a good possibility that energy could be lost there.

16. ### hansdaValued Senior Member

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YES.

YES.
100% and 99.9999...upto infinite number of 9' % are same.
There is no missing part.
The 4th missing part is a single point, which is dimensionless.It does not have any area. So it does not make any difference as far as area is concerned.

17. ### hansdaValued Senior Member

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The center point is a single point which is dimensionless. As per the definitions of mathematics, a single point does not have any area. So, the center point does not make any difference as per as area distribution or division is concerned.

18. ### someguy1Registered Senior Member

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That explains your point of view. If you'd taken some actual grad-level math you would understand the difference between a measure-preserving transformation and a distance preserving one. You would understand that geometry is the study of groups of transformations that preserve some quantity you're interested in.

It's interesting that I pegged you earlier as a physics guy. Applied math, same thing. You have spent a lot of time pushing symbols around but you've never been forced to drill down to the definitions and apply them. You've never really been forced to think about what you're doing. Otherwise you'd realize that there is more than one type of geometrical transformation; and that different types of transformations preserve different quantities.

From John Baez's crackpot index:

10 points for pointing out that you have gone to school, as if this were evidence of sanity.

http://math.ucr.edu/home/baez/crackpot.html

Tell me this. If I have a square of measure one, and a circle of measure 1 ... are they the same shape? After all, they have the same area. And you are claiming that preserving area is the only thing that matters.

19. Coming from someone who doesn't know how to solve an 8-th grade geometry problem of circle trisection, this is rich.

As a matter of fact, I did. The difference between the two of us is that I can make use of the math I learned whereas you are obviously incapable of doing anything useful with it.

Back to your fixation with "what do we do with the center of the circle", I see. For your information, I had a lot of advanced classes, including group theory.

Now you are being outright stupid or dishonest, or both. The question is : "if you assign the center of the circle to one of the three slices, is there any difference between the three slices"? You don't have to answer that, the question is rhetorical and I am not interested in your persistent droning.

20. ### Quantum QuackLife's a tease...Valued Senior Member

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23,326
I know I may be way out of turn but does the following image [posted earlier] provide a possible solution. Certainly it appears that Tach is referring to it if not with out wishing to.

Clearly by using this "infinitesimal approach" to zero the central point CAN be shared equally amongst all 3 segments.
Maybe this is what Tach is alluding to.. although he very rarely explains past his usual ULTRA defensive flaming and trolling.
"Yeah... I know there are bucket loads of axiomatic uses and abuses to block or obstruct such a notion but it seem pretty clear to me that it provides a solution to some of the problems maths has in reconciling with reality."

"There's a hole in my bucket, dear Henry, dear Henry"

21. ### someguy1Registered Senior Member

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It's astonishing to me that you claim to have a graduate degree in the mathematical sciences, yet you don't understand the basic concept of a disjoint partition. If I were you I would demand a refund from the institution that granted you an undergraduate degree, which is where you should have learned this.

22. I understand it, I even gave you the definition many posts ago. But this is not what we are talking about, we are talking about your inability to solve a simple geometry problem. Unlike you, I am not astonished by that. Heck, even the Quack managed to understand it, why can't you?

23. Try explaining it to someguy1. He is still struggling with the solution.

Actually, you are lying, I explained it in great detail to someguy1, for some reason, it is not sinking in for him. Do you know how to do the partition using just a compass and a ruler? I think I asked you this several times but you evaded each time.