Wikipedia:Reference desk/Archives/Mathematics/2016 November 2

= November 2 =

Given a series of binary choices, how can I know whether they are independent?
How can we assess whether a series is random stuff or has some tendencies? An example of the former is the choice red/black or even/odd from a roulette. An example of the latter would be win/lost results of a tennis player. In this case, he could be in a winning or losing streak, and his results cannot be treated as independent.

If only the results are given (which are binary, to simplify things) and we do not have any information about the process that generated them, can we still determine in which series the results are independent and in which they are dependent or have tendencies?--Pedia wikipedia (talk) 21:38, 2 November 2016 (UTC)
 * There's no single conclusive way to determine this, but a variety of randomness tests are available and useful in practice. -- Meni Rosenfeld (talk) 22:23, 2 November 2016 (UTC)


 * See also hot hand fallacy—some of the references therein may be helpful. Loraof (talk) 22:34, 2 November 2016 (UTC)


 * almost surely discusses some of the issues surrounding the word "know". Robinh (talk) 20:11, 5 November 2016 (UTC)

Is infinitesimal not part of the real number system?
I have read the article Infinitesimal but I could not figure out from reading it, if infinitesimal is part of the real number system or not. Can someone please clear it up for me. Oh! And is it part of the complex number system? 175.45.116.104 (talk) 22:11, 2 November 2016 (UTC)
 * There are no nonzero infinitesimals within the real numbers (This is their so-called Archimedean property). Not within the complex numbers, either. They exist in some other structures, such as the Surreal numbers. -- Meni Rosenfeld (talk) 22:21, 2 November 2016 (UTC)