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List of unsolved problems in astronomy. This article is a list of notable unsolved problems in astronomy. Problems may be theoretical or experimental. Theoretical problems result from inability of current theories to explain observed phenomena or experimental results. Experimental problems result from inability to test or investigate a proposed ...
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.
A Langford pairing for n = 4. In combinatorial mathematics, a Langford pairing, also called a Langford sequence, is a permutation of the sequence of 2 n numbers 1, 1, 2, 2, ..., n, n in which the two 1s are one unit apart, the two 2s are two units apart, and more generally the two copies of each number k are k units apart.
The case n = 2 is the axiom of pairing with A = A 1 and B = A 2. The cases n > 2 can be proved using the axiom of pairing and the axiom of union multiple times. For example, to prove the case n = 3, use the axiom of pairing three times, to produce the pair {A 1,A 2}, the singleton {A 3}, and then the pair {{A 1,A 2},{A 3}}.
The following are the headers for Hilbert's 23 problems as they appeared in the 1902 translation in the Bulletin of the American Mathematical Society. [1] 1. Cantor's problem of the cardinal number of the continuum. 2. The compatibility of the arithmetical axioms. 3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes.
Unsolved problems in computer science; Unsolved problems in information theory; Social sciences and humanities. Problems in philosophy; Unsolved problems in economics; Unsolved problems in fair division; See also. Cold case (unsolved crimes) List of ciphertexts; List of hypothetical technologies; List of NP-complete problems; List of paradoxes
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
Toyota’s chairman Akio Toyoda will be facing some disgruntled shareholders this week, as two major proxy groups demand a vote against keeping the grandson of the founder on its board. The vote ...