Wikipedia:Reference desk/Archives/Mathematics/2008 November 27

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November 27

Diophantine

Hi all, I am trying to this problem:

• given n,K , how many soultions (in while numbers) there is to : x1+...+xn=K

I am prrety sure there is a name to this problem, but i cant find it. Thanks 193.34.56.1 (talk) 10:42, 27 November 2008 (UTC)

In whole numbers, i.e., integers? There are infinitely many solutions, as long as n is at least 2. Just take (K − k) + k + 0 + … + 0 for any integer k. — Emil J. 11:14, 27 November 2008 (UTC)

If it's Diophantine, it will be integers. I suspect the problem is "How many solutions are there for a given K?". We have an article, Partition (number theory), that might help. --Tango (talk) 11:24, 27 November 2008 (UTC)

Thank you Tango. —Preceding unsigned comment added by 193.34.56.1 (talk) 11:27, 27 November 2008 (UTC)

If the order of the variables matters, see instead Composition_(number_theory). McKay (talk) 07:26, 29 November 2008 (UTC)

Philosophy of probability

Suppose an unique event (with two possible outcomes) only occurs once. Does it really have a probability? 122.107.203.230 (talk) 13:13, 27 November 2008 (UTC)

It doesn't have a frequency probability, it does have a bayesian probability. See also, probability interpretations and philosophy of probability. --Tango (talk) 13:46, 27 November 2008 (UTC)

It is a question of language rather than a question of mathematics. The concept of probability was earlier called degree of probability. The words likelihood and credibility are sometimes used regarding some unknown fact or a dubious assertion. So you may want to discuss the (degree of) probability that a throw of dice show 6, the (degree of) likelihood that You (as opposed to anybody else) will make president of the USA, and the (degree of) credibility that Jesus has risen from the dead. When different persons have got different data, the likelihood and the credibility may get different (subjective) values. See perhaps also Fuzzy logic. Bo Jacoby (talk) 11:21, 28 November 2008 (UTC).

If you're a Platonist then it has a probability, you just don't have the statistics to have an idea of what it is with any degree of certainty. I don't suppose we'll have anything like Bell's inequality about something like this! Dmcq (talk) 14:19, 28 November 2008 (UTC)

One of the most important examples of this is the probability that life would have evolved on Earth. The best approach here may be to combine sub-probabilites for events like the natural formation of amino acids, the probability of those amino acids forming proteins, etc. StuRat (talk) 16:13, 28 November 2008 (UTC)

"The probability that life would have evolved on Earth" must be one, because we do know that life has evolved on Earth. "The probability that life would have evolved on another Earth-like planet" is |{earthlike planets with life}|/|{earthlike planets}|. This number is reasonably well defined, albeit unknown. "The probability that life would have evolved on Mars" may be rephrased into "The likelihood that life has evolved on Mars" in order to make sense. This number depend on our state of knowledge. Bo Jacoby (talk) 11:29, 29 November 2008 (UTC).

I was using "would have" to mean the probability before the event occurred. I would say "The probability that life did evolve on Earth" to mean the probability as measured now. There is, however, some slight possibility that life began elsewhere ("exogenesis") and was somehow transported to Earth, so the probability is something less than 1, even in this case. StuRat (talk) 14:52, 29 November 2008 (UTC)