Yes when the rope drawn from the "north pole" of the football is paralell to the floor you have spanned the second domension, too. Infinity is where the two paralell lines cross.

The problem is, you would not have enough money to buy that rope as log as it is not a free lunch. What about the material to build the rope? Would there be enough in our universe?

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You keep me in stitches kgun, <smile> and if it weren’t for my good sense of humor then I would have vanished <dramatic prose> but alas, there is more area to tread. </drama>

I would have to understand the ball and string example to call it proof! The problem IMO is that if infinity is where the two cross then that establishes a definite point which contradicts the concept of infinity!

Now since I’m not a mathmagician I have to question the following comment…

Easy enough,… In the example the given number is ½ x the reciprocal number 2 = 1
Umm, considering the infinity problem deepsand proposes… first, any number times zero equals zero and second, how can an infinite number, which isn’t really a number because there is no number to define it or it would be a finite number, be in the equation?
If the given number 0 x the imagined infinite unknown number = 0 then this can’t be reciprocally correct because it should be a result of one according to the definition.
Can you explain that? ( keep in mind that talking slower isn’t going to help )

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1. That infinite is the inverse of zero is not the result of a computation, but a definition made by some mathematicians (if I remember correctly). Whether it is an useful definition is another discussion.
2. The usual rules of calculus do not apply to infinite. See above posts.
3. The complete real line is the union of the real line and +/- infinity.

Did I call it a proof or a "proof"? If I wrote proof above, it should be "proof"

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Therein lies the problem; the intersection occurs, not at a finite, i.e. not definite, distance, but at an infinite one.

From Wikipedia, we have:

For integers, fractions, real and complex numbers, multiplication has certain properties:

Commutative property
The order in which two numbers are multiplied does not matter:.

Associative property
Problems solely involving multiplication are invariant with respect to order of operations:

Distributive property
Holds with respect to addition over multiplication. This identity is of prime importance in simplifying algebraic expressions:

Identity element
of multiplication is 1; anything multiplied by one is itself. This is known as the identity property:

Zero element
Anything multiplied by zero is zero. This is known as the zero property of multiplication:

Inverse property
Every number x, except zero, has a multiplicative inverse, , such that .

Order preservation
Multiplication by a positive number preserves order: if a > 0, then if b > c then ab > ac. Multiplication by a negative number reverses order: if a < 0 and b > c then ab < ac.

• Negative one times any number is equal to the negative of that number.

• Negative one times negative one is positive one.

Other mathematical systems that include a multiplication operation may not have all these properties. For example, multiplication is not, in general, commutative for matrices and quaternions.

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Matrices are a non Abelian group.

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Depends on the "material."

Allowing for virtual particles, an infinitely large vacuum contains an infinitely large supply.

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Thanks very much for that link; rep. added to as show of gratitude.

I'd had that site bookmarked on a machine whose HD died, and thus lost countless links to valuable resources, of which many remain un-recalled.

Such now number 1 less.

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Thank you. That say that some posters appriciate what I write. There are three Norwegian mathematicians that have had mathematical Groups named after their last name. In addition to Abel mentioned above, you have

• Sophus Lie - Wikipedia, the free encyclopedia / Lie group - Wikipedia, the free encyclopedia (lived in the town where I live).
• Peter Ludwig Mejdell Sylow - Wikipedia, the free encyclopedia / PlanetMath: Sylow p-subgroup / http://picard.ups-tlse.fr/~mcshane/L...-groups-04.pdf

Sophus Lie may be more known for Lie algebra - Wikipedia, the free encyclopedia that is said to simplificate Einsteins Theory of relativity among other things. I have not seen a proof of that. Most probably I would be too impatient to read it.

I am as written above a "quasi" mathematician that have not followed proofs expanding more than 11 book pages. I have heard of proofs expanding 400 pages and other proofs taken two semesters to proof for students.

I stand by my "football proof" Q.E.D.

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How about 10,000 pages?

From http://ocw.mit.edu/NR/rdonlyres/Math...sophusl1_1.pdf , we have:

Finite groups.
Let g be a simple Lie algebra over C, (Xi) a basis and c the structural constants given by [X,,Xk] = CkX i. i A theorem of Chevalley [3] states that the basis Xi can be chosen such that the c}k are integers ([6], p. 195). While the theorem is not particularly difficult to prove it has major implications. In particular, if we read the ck mod p we have a Lie algebra over a field of characteristic p. By considering the finite fields and the automorphism groups of the ensuing Lie algebras Chevalley constructed the simple finite groups which correspond to the Killing-Cartan classification. These groups and certain twisted analogs are called finite groups of Lie type. Several simple finite groups did not fit into this construction. However, it became more and more difficult to construct such groups which therefore acquired the designation sporadic. Specialist began to suspect that there would only be finitely many of those and that all finite simple groups could therefore be explicitly constructed. This enormous project has now been completed (1981) with the following result.

Main theorem. The simple groups of Lie type and 26 others explicitly constructed sporadic groups of order from 7920 to 246 · 320 .59 76.112 133 17.19.23- 29-31-41 47-59 -71, constitute all finite simple groups. The largest of these 26 is called "The Friendly Giant" or "The Monster". The original proof is the result of a number of journal articles of total length over 10, 000 pages.

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<quote>
Lie died in 1899 at the age of 56, long before the influence of Lie algebras in mathematics was realized,
</quote>
Interesting.

Reminds me of my Mathematics professor Raphael Høegh-Krohn, LiUB - lokal katalog=

that died too young, that said the following. Mathematicis is a collection of trivialities. Each step is trivial.

I think he worked on non-linear partial differential equations, distributions and generalized functions.

Related work with another of my teachers, Tom Lindstrøm: http://projecteuclid.org/DPubS/Repos...ams/1183554202

"Default" Scroll down to Michael Oberguggenberger, Universitaet Innsbruck: "Nonlinear SDEs: Colombeau solutions and pathwise limits"

I had an other mathematics professor that said that the most complex computer program was simple compared to mathematics. But when a proof is more than 10 000 pages large and a computer programs spans millions of lines of code, it is not trivial longer.

As far as I know, that is a main difference between Internet Explorer and Opera. A lot of programmers at Microsoft combine their code segments into an overall program. Far less programmers work on Opera. For that reason, it is obvious that it is much easier to introduce new features and change errors in Opera that in Internet Explorer. Regarding security, this is of utmost importance. Another reason why security upgrades are much more frequent in Opera than in Internet Explorer. It may be very difficult to change the security model of security zones in IE (that IMO is false security).

Seems that we have a tendency to be ahead of time. Econometricians seem to agree that my teacher at the economics institute of Oslo, Nobel pize winner Trygve Haavelmo was 50 years ahead of time. I read his docotoral theis, "The probability approach in Econometrics." That is still very relevant, and I have much use of what I learned there. He is also known for what is called the Haavelmo Distribution, a very important concept today in econometrics.

What about object oriented programming. Teachers at the institute for information science told me that it took 20 years befor foreigners understood what they were talking about.

How Object-Oriented Programming Started My be one reason that the Danish member was so very aggressive in his posts.

The Mjølner System: Online Information

I know his comments if he read this post

May be the best had been not to write it.

Sometimes clear misinformation has to be corrected (post #6 and #22):

PHP OOP General design practices - SitePoint Forums

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Did you catch the show on the guy from England they call the "brain man" - you would appreciate this guy Kjell, he can calculate virtually anything in his head, ie. square root of 6587, 78 raised to the fourth power, all in seconds. Really quite amazing. They were wondering how he did it.

They even had an interesting side story about children in Japan. In Japan they teach children to perform math using an abacus. The children get adept at the use of the abacus and in a manner similar to a spelling bee, they actually hold math competitions where the children are not permitted to actually use the abacus, neverthless the young man who won the competition actually has a mental image of the abacus and 'operates' the abacus with his fingers which are moving and manipulating the 'mental' abacus. Really quite amazing.

In any event they were trying to figure out how he was doing it and they concluded that indeed his brain was simply doing the calculation quite naturally.

His skills translated into other areas as well. He spent approximately one week in Iceland and after that week was able to speak Icelandic quite fluently and to conduct an interview in the language (he had no prior knowledge of the language) (of course English and Icelandic are on the Germanic line of languages, but still!)

They also brought him to a casino, but alas he had no luck there!

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I have sensed some of these individuals. That is why I call myself a "quasi" mathematician. If some of them joined WPW, I could use that as an excuse.

And I am an economist. I have not met economists that I can not talk with, but I have met mathematicans that spoke "greek" to me.

If what I heard is correct, Abel's Dr. Thesis of 6 pages were accepted, but it is difficult to accept, so most probably it is wrong rumour. Dr, Theses use to span hundreds of pages.

If you look at one of the above links, I participated on a seminar on Stchastic Analysis, where I gave a 30 minute lecture on "Determinism and stochastics in Economics".

I think I had problems understanding 5 % of what was said there.

Now it is EM in Soccer. I will watch the match

Portugal - Tukey.

For me there are many great sports, but no like soccer. My favourite team is Brazil when they play Samba football.

I also watched Hillary's exit. I noticed the following words.

"I did not plan this party, but enjoy the audience".

May be a good sentencene to remember.

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I always like Hilary Clintons theme tune..."I get knocked down but I get up again"
it was a bit premature maybe...but who knows...maybe she will make a comeback some time...I am in UK so I havent taken all that much notice of what she stands for (...disclaimer...)

YouTube - Tubthumping (I Get Knocked Down) Lyrics

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And just 4 Kjun

YouTube - Football!!!!!!! (Chumbawamba - I Get Knocked Down)

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Thank you.

Some of the best moments in that movie clip.

May be the best, that Colombian Keeper.

Definitely better use of the football than using it for my "football proof" of how infinite infinite is.

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