Wikipedia:Reference desk/Archives/Mathematics/2012 August 3

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August 3

Name of a Logical Equivalence

I am trying to remember the name of the following logical equivalence: If A, then B. Hence, if not(B), then not(A).

I know the above relation has a name in Logic; but I cannot remember it. It's on the tip of my tongue. Any help? _{Hisham1987 (talk) 00:41, 3 August 2012 (UTC)}

Contrapositive. Looie496 (talk) 01:52, 3 August 2012 (UTC)

or maybe modus tollens? Rckrone (talk) 01:53, 3 August 2012 (UTC)

Yes! I was looking for either of these two words. Thanks! _{Hisham1987 (talk) 02:23, 3 August 2012 (UTC)}

Resolved

Can you tell if a series of numbers is chaotic?

If something are picking numbers and you don't know if there are chaotic, can you know just analyzing the output? (Given, for example, that you know that they are all integers between 0 and 9). Or do you have to analyze the machine producing the random numbers? — Preceding unsigned comment added by 80.58.205.34 (talk) 11:08, 3 August 2012 (UTC)

First of all, don't confuse a series with a sequence. I assume you're asking about a sequence, e.g. (1, 2, 3, 2, 1, …) and not a series, e.g. 1 + 2 + 3 + 2 + 1 + …. You'd have to look at the algorithm that the machine is using. It's very easy to contrive a sequence where, say, the first 10¹⁰¹⁰ number have no pattern, but then the sequence settles down to being all 0s. You'd be dead before you reached the point where the sequence settles down. — Fly by Night (talk) 12:27, 3 August 2012 (UTC)

Surely any true random number generator can possibly produce any seemingly regular sequence, thereby appearing to be non-random? Rojomoke (talk) 12:34, 3 August 2012 (UTC)

Exactly. Looking at the outputs doesn't give you a definitive answer although, as Sławomir mentions, there are statistical methods that allow you to comment on the likelihood of the outputs being "truly random". To be sure, you'd need to know about the machine's inner workings. — Fly by Night (talk) 18:51, 3 August 2012 (UTC)

If by "chaotic" you mean "random", there are many statistical tests for randomness. See Diehard test. Sławomir Biały (talk) 14:26, 3 August 2012 (UTC)

If you mean chaos as in chaos theory then yes you can normally tell them apart and even separate the change into a component due to chaos and a random part provided neither part is so large it swamps the other. Chaos is deterministic and random isn't. I see there is a section about this at Chaos_theory#Distinguishing_random_from_chaotic_data though it doesn't say that much, and I've seen such an analysis put to everyday practical use with sampling and rejecting batches of a product in a factory. Dmcq (talk) 22:18, 3 August 2012 (UTC)