By Catherine Cavagnaro, William T. Haight II
Containing greater than 1,000 entries, the Dictionary of Classical and Theoretical arithmetic makes a speciality of mathematical phrases and definitions of serious significance to working towards mathematicians and scientists. This single-source reference offers operating definitions, meanings of phrases, similar references, and an inventory of other phrases and definitions. The dictionary is certainly one of 5 constituent works that make up the casebound CRC entire Dictionary of arithmetic.
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Extra info for Dictionary of Classical and Theoretical Mathematics (Comprehensive Dictionary of Mathematics)
The conical surface consists of two concave pieces positioned symmetrically about the vertex. It is quadric if the directrix is a conic. A circular conical surface is one whose directrix is a circle and whose vertex is on the line perpendicular to the plane of the circle and passing through the center of the circle. , (A11 ∨ · · · ∨ A1m1 ) ∧ · · · ∧ (An1 ∨ · · · ∨ Anmn ), where each Aij , 1 ≤ i ≤ n, 1 ≤ j ≤ mi , is either a sentence symbol or the negation of a sentence symbol. Every well-formed propositional formula is logically equivalent to one in conjunctive normal form.
Xn , the tape is initially set to . . B1x1 +1 B1x2 +1 B . . B1xn +1 B . . , where 1k indicates a string of k 1s, one symbol 1 per cell, . . B1x1 +1 indicates that all cells to the left of the initial 1 on the tape are blank, and 1xn +1 B . . indicates that all cells to the right of the last 1 on the tape are blank. The reading head is positioned on the leftmost 1 on the tape, and the machine is set to the initial state q0 . The output of the function (if any) is the number of 1s on the tape when the machine halts, after executing the program, if it ever halts.
An ) is true or false. This decision problem is solvable if R is recursive (computable) as a relation; otherwise it is unsolvable. There are many famous decision problems. Hilbert’s Tenth Problem asks if there is an effective procedure which, given a Diophantine equation p(x1 , . . , xn ) = 0, where p is a polynomial with integer coefficients, determines whether or not there is an integer solution. It was proved by results of Matijaseviˇc (1970) and Davis, Putnam, and Robinson (1961) that Hilbert’s Tenth Problem is not solvable.
Dictionary of Classical and Theoretical Mathematics (Comprehensive Dictionary of Mathematics) by Catherine Cavagnaro, William T. Haight II