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Strategies & Market Trends : ahhaha's ahs -- Ignore unavailable to you. Want to Upgrade?


To: ahhaha who wrote (555)12/8/2000 10:18:27 PM
From: BilowRead Replies (1) | Respond to of 24758
 
Hi ahhaha; Thanks for your quick reply!

Re "I am a mathematician. If Pi is exact at what fraction does it resolve? Computability isn't a criterion for exactness, because the computation could take forever to complete and thus, it never does, and so Pi isn't exact."

Interesting question... How does one "resolve" Pi to a "fraction"... First "resolve":

Definition of Resolve:
13.Mathematics. To separate (a vector, for example) into coordinate components.

dictionary.com

This doesn't seem to make a lot of sense. Perhaps by "at what fraction does it resolve" you mean to ask what fraction is equal to Pi. I suspect that there are simpler solutions to this deep and intriguing riddle, but one that I came up with is this equation:

Pi = (Pi * 7)/(3+4).

Clearly the right hand side consists of a "fraction", and the right side is Pi. Therefore, Pi is expressible as a fraction.

Definition of Fraction
1.Mathematics. An expression that indicates the quotient of two quantities.

dictionary.com

Definition of Quotient
Mathematics: The number obtained by dividing one quantity by another. In 45 ÷ 3 = 15, 15 is the quotient.

dictionary.com

Definition of Number
b.A member of any of the further sets of mathematical objects, such as negative integers and real numbers, that can be derived from the positive integers by induction.

dictionary.com

Is Pi a "number"? Sure it is:

Definition of Pi
2.Mathematics. A transcendental number, approximately 3.14159, represented by the symbol , that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions.

dictionary.com

Maybe the thought that you were intending to express was likely that Pi was not equal to any rational number, which is well known. On the other hand, Pi is certainly equal to any number of fractions.

Also of interest:

Definition of Transcendental
(adj) 4 b.Not expressible as an integer or as the root or quotient of integers. Used of numbers, especially nonrepeating infinite decimals.

dictionary.com

Definition of Real Number
dictionary.com

Definition of Irrational Number
Any real number that cannot be expressed as an integer or as a ratio between two integers.

dictionary.com

-- Carl

P.S. I did give definitions for "odds" and "probability", not only that, I gave a reference for them. Here they are again:

Definition of "Probability"
3. b.Statistics. A number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences.

dictionary.com

Definition of "Odds"
2. a.The ratio of the probability of an event's occurring to the probability of its not occurring.

dictionary.com

Probably the funniest thing in your post (other than your claim to be a mathematician, and believe me, I know mathematicians, and you ain't one), was this statement: "Odds are exact. Probability isn't. #reply-14979766

Since the above two above definitions clearly state that odds are defined as ratios of probabilities, one naturally wonders how it is that taking the ratio of two numbers that are not exact (i.e. the probabilities) gives you a result that is exact (i.e. the odds). Any explanation? (G)

-- Carl