Number

The word ``number'' is a general term which refers to a member of a given (possibly ordered) Set. The meaning of ``number'' is often clear from context (i.e., does it refer to a Complex Number, Integer, Real Number, etc.?). Wherever possible in this work, the word ``number'' is used to refer to quantities which are Integers, and ``Constant'' is reserved for nonintegral numbers which have a fixed value. Because terms such as Real Number, Bernoulli Number, and Irrational Number are commonly used to refer to nonintegral quantities, however, it is not possible to be entirely consistent in nomenclature.

See also Abundant Number, Ackermann Number, Algebraic Number, Almost Perfect Number, Amenable Number, Amicable Numbers, Antimorphic Number, Apocalypse Number, Apocalyptic Number, Armstrong Number, Arrangement Number, Bell Number, Bernoulli Number, Bertelsen's Number, Betrothed Numbers, Betti Number, Bezout Numbers, Binomial Number, Brauer Number, Brown Numbers, Cardinal Number, Carmichael Number, Catalan Number, Cayley Number, Centered Cube Number, Centered Square Number, Chaitin's Number, Chern Number, Choice Number, Christoffel Number, Clique Number, Columbian Number, Complex Number, Computable Number, Condition Number, Congruent Numbers, Constructible Number, Cotes Number, Crossing Number (Graph), Crossing Number (Link), Cubic Number, Cullen Number, Cunningham Number, Cyclic Number, Cyclomatic Number, D-Number, de Moivre Number, Deficient Number, Delannoy Number, Demlo Number, Diagonal Ramsey Number, e-Perfect Number, Eban Number, Eddington Number, Edge Number, Enneagonal Number, Entringer Number, Erdös Number, Euclid Number, Euler's Idoneal Number, Euler Number, Eulerian Number, Euler Zigzag Number, Even Number, Factorial Number, Fermat Number, Fibonacci Number, Figurate Number, G-Number, Genocchi Number, Giuga Number, Gnomic Number, Gonal Number, Graham's Number, Gregory Number, Hailstone Number, Hansen Number, Happy Number, Harmonic Divisor Number, Harmonic Number, Harshad Number, Heegner Number, Heesch Number, Helly Number, Heptagonal Number, Heterogeneous Numbers, Hex Number, Hex Pyramidal Number, Hexagonal Number, Homogeneous Numbers, Hurwitz Number, Hypercomplex Number, Hyperperfect Number, i, Idoneal Number, Imaginary Number, Independence Number, Infinary Multiperfect Number, Infinary Perfect Number, Irrational Number, Irreducible Semiperfect Number, Irredundant Ramsey Number, j, Kaprekar Number, Keith Number, Kissing Number, Knödel Numbers, Lagrange Number (Diophantine Equation), Lagrange Number (Rational Approximation), Large Number, Least Deficient Number, Lehmer Number, Leviathan Number, Liouville Number, Logarithmic Number, Lucas Number, Lucky Number, MacMahon's Prime Number of Measurement, Markov Number, McNugget Number, Ménage Number, Mersenne Number, Motzkin Number, Multiplicative Perfect Number, Multiply Perfect Number, Narcissistic Number, Natural Number, Near Noble Number, Nexus Number, Niven Number, Noble Number, Nonagonal Number, Normal Number, NSW Number, Number Guessing, Oblong Number, Octagonal Number, Octahedral Number, Odd Number, Ore Number, Ordinal Number, Pentagonal Number, Pentatope Number, Perfect Digital Invariant, Perfect Number, Persistent Number, Pluperfect Number, Plus Perfect Number, Plutarch Numbers, Polygonal Number, Pontryagin Number, Poulet Number, Powerful Number, Practical Number, Primary, Primitive Abundant Number, Primitive Pseudoperfect Number, Primitive Semiperfect Number, Pseudoperfect Number, Pseudorandom Number, Pseudosquare, Pyramidal Number, Q-Number, Quasiperfect Number, Ramsey Number, Rational Number, Real Number, Rencontres Number, Recurring Digital Invariant, Repfigit Number, Rhombic Dodecahedral Number, Riesel Number, Rotation Number, RSA Number, Sarrus Number, Schröder Number, Schur Number, Secant Number, Segmented Number, Self-Descriptive Number, Self Number, Semiperfect Number, Sierpinski Number of the First Kind, Sierpinski Number of the Second Kind, Singly Even Number, Skewes Number, Small Number, Smith Number, Smooth Number, Sociable Numbers, Sprague-Grundy Number, Square Number, Square Pyramidal Number, Star Number, Stella Octangula Number, Stiefel-Whitney Number, Stirling Cycle Number, Stirling Set Number, Størmer Number, Sublime Number, Suitable Number, Sum-Product Number, Super-3 Number, Super Catalan Number, Superabundant Number, Superperfect Number, Super-Poulet Number, Tangent Number, Taxicab Number, Tetrahedral Number, Transcendental Number, Transfinite Number, Triangular Number, Tribonacci Number, Trimorphic Number, Truncated Octahedral Number, Truncated Tetrahedral Number, Twist Number, U-Number, Ulam Number, Undulating Number, Unhappy Number, Unitary Multiperfect Number, Unitary Perfect Number, Untouchable Number, Vampire Number, van der Waerden Number, VR Number, Weird Number, Whole Number, Woodall Number, Z-Number, Zag Number, Zeisel Number, Zig Number

References

Numbers

Barbeau, E. J. Power Play: A Country Walk through the Magical World of Numbers. Providence, RI: Amer. Math. Soc., 1997.

Bogomolny, A. ``What is a Number.'' http://www.cut-the-knot.com/do_you_know/numbers.html.

Borwein, J. and Borwein, P. A Dictionary of Real Numbers. London: Chapman & Hall, 1990.

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, 1996.

Dantzig, T. Number: The Language of Science, 4th rev. ed. New York: Free Press, 1985.

Davis, P. J. The Lore of Large Numbers. New York: Random House, 1961.

Frege, G. Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl. New York: Georg Olms, 1997.

Frege, G. Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number. Evanston, IL: Northwestern University Press, 1968.

Ifrah, G. From One to Zero: A Universal History of Numbers. New York: Viking, 1987.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, 1983.

Phillips, R. Numbers: Facts, Figures & Fiction. Cambridge, England: Cambridge University Press, 1994.

Russell, B. ``Definition of Number.'' Introduction to Mathematical Philosophy. New York: Simon and Schuster, 1971.

Smeltzer, D. Man and Number. Buchanan, NY: Emerson Books, 1974.

Wells, D. W. The Penguin Dictionary of Curious and Interesting Numbers. Harmondsworth, England: Penguin Books, 1986.