Meaning of CANTOR
Pronunciation:   'kantur



Matching Terms:   canto, canton, canton crape, canton crepe, canton flannel, canton ginger, canton river, cantonal, cantoned, cantonese, cantonese dialect, cantonize, cantonment, cantoon, cantoral, cantoris

Computing Dictionary 

 Definition:   1. A mathematician. Cantor devised the diagonal proof of the uncountability of the real numbers: Given a function, f, from the natural numbers to the real numbers, consider the real number r whose binary expansion is given as follows: for each natural number i, r's ith digit is the complement of the ith digit of f(i). Thus, since r and f(i) differ in their ith digits, r differs from any value taken by f. Therefore, f is not surjective (there are values of its result type which it cannot return). Consequently, no function from the natural numbers to the reals is surjective. A further theorem dependent on the axiom of choice turns this result into the statement that the reals are uncountable. This is just a special case of a diagonal proof that a function from a set to its power set cannot be surjective: Let f be a function from a set S to its power set, P(S) and let U = (x in S: x not in f(x)). Now, observe that any x in U is not in f(x), so U != f(x); and any x not in U is in f(x), so U != f(x): whence U is not in (f(x) : x in S). But U is in P(S). Therefore, no function from a set to its powerset can be surjective. 2. An objectoriented language with finegrained concurrency. [Athas, Caltech 1987. "Multicomputers: Message Passing Concurrent Computers", W. Athas et al, Computer 21(8):924 (Aug 1988)]. 

Thesaurus Terms 

 Related Terms:   alto, aria singer, baal kore, baritenor, baritone, bass, basso, basso buffo, basso cantante, basso profundo, blues singer, canary, cantatrice, caroler, chanter, chantress, chief rabbi, choir chaplain, choirmaster, choral director, chorister, coloratura soprano, comic bass, contralto, countertenor, crooner, deep bass, diva, dramatic soprano, Heldentenor, heroic tenor, high priest, hymner, improvisator, kohen, lead singer, Levite, lieder singer, Meistersinger, melodist, mezzosoprano, minister of music, opera singer, precentor, priest, prima donna, psalm singer, rabbi, rabbin, rockandroll singer, scribe, singer, singstress, songbird, songster, songstress, soprano, tenor, torch singer, vocalist, vocalizer, voice, warbler, yodeler 
 

