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A free group of rank k clearly has subgroups of every rank less than k. Less obviously, a (nonabelian!) free group of rank at least 2 has subgroups of all countable ranks. The commutator subgroup of a free group of rank k > 1 has infinite rank; for example for F(a,b), it is freely generated by the commutators [a m, b n] for non-zero m and n.
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Lolicon is a Japanese abbreviation of "Lolita complex" (ロリータ・コンプレックス, rorīta konpurekkusu), [5] an English-language phrase derived from Vladimir Nabokov's novel Lolita (1955) and introduced to Japan in Russell Trainer's The Lolita Complex (1966, translated 1969), [6] a work of pop psychology in which it is used to denote attraction to pubescent and pre-pubescent girls. [7]
Worksheet generators are often used to develop the type of worksheets that contain a collection of similar problems. A worksheet generator is a software program that quickly generates a collection of problems, particularly in mathematics or numeracy. Such software is often used by teachers to make classroom materials and tests.
See Waring's problem and the related Waring–Goldbach problem on sums of powers of primes. Hardy and Littlewood listed as their Conjecture I: "Every large odd number (n > 5) is the sum of a prime and the double of a prime". [31] This conjecture is known as Lemoine's conjecture and is also called Levy's conjecture.
The Two Generals' Problem appears often as an introduction to the more general Byzantine Generals problem in introductory classes about computer networking (particularly with regard to the Transmission Control Protocol, where it shows that TCP can't guarantee state consistency between endpoints and why this is the case), though it applies to ...
Another related problem is the meta-Newcomb problem. [20] The setup of this problem is similar to the original Newcomb problem. However, the twist here is that the predictor may elect to decide whether to fill box B after the player has made a choice, and the player does not know whether box B has already been filled.
The problem of free will, in this context, is the problem of how choices can be free, given that what one does in the future is already determined as true or false in the present. [52] Theological determinism The idea that the future is already determined, either by a creator deity decreeing or knowing its outcome in advance.
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