Cantor
1. A mathematician. Cantor devised the diagonal proof of the uncountability of the href="module.php?name=Lexikon&file=search&eid=1&query=real numbers">real numbers: Given a function, f, from the href="module.php?name=Lexikon&file=search&eid=1&query=natural numbers">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 i-th digit is the complement of the i-th digit of f(i). Thus, since r and f(i) differ in their i-th digits, r differs from any value taken by f. Therefore, f is not href="module.php?name=Lexikon&file=search&eid=1&query=surjective">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 href="module.php?name=Lexikon&file=search&eid=1&query=axiom of choice">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 href="module.php?name=Lexikon&file=search&eid=1&query=power set">power set cannot be surjective: Let f be a function from a set S to its power set, P(S) and let U = href="x"> x in S: x not in f. 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 href="x"> f. But U is in P(S). Therefore, no function from a set to its power-set can be surjective. 2. An href="module.php?name=Lexikon&file=search&eid=1&query=object-oriented language">object-oriented language with fine-grained href="module.php?name=Lexikon&file=search&eid=1&query=concurrency">concurrency. [Athas, Caltech 1987. "Multicomputers: Message Passing Concurrent Computers", W. Athas et al, Computer 21(8):9-24 (Aug 1988)]. (1997-03-14) In addition suitable contents:
[ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=396">ag ] [ href="module.php?name=Lexikon&op=content&tid=411">ai ] [ href="module.php?name=Lexikon&op=content&tid=433">al ] [ href="module.php?name=Lexikon&op=content&tid=531">alt ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=800">as ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=1013">axiom ] [ href="module.php?name=Lexikon&op=content&tid=1025">B ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1181">be ] [ href="module.php?name=Lexikon&op=content&tid=1269">bi ] [ href="module.php?name=Lexikon&op=content&tid=1298">binary ] [ href="module.php?name=Lexikon&op=content&tid=1368">bj ] [ href="module.php?name=Lexikon&op=content&tid=1606">bs ] [ href="module.php?name=Lexikon&op=content&tid=1695">by ] [ href="module.php?name=Lexikon&op=content&tid=1708">C ] [ href="module.php?name=Lexikon&op=content&tid=1724">ca ] [ href="module.php?name=Lexikon&op=content&tid=1844">case ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2099">ci ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2330">com ] [ href="module.php?name=Lexikon&op=content&tid=2438">complement ] [ href="module.php?name=Lexikon&op=content&tid=2490">Computer ] [ href="module.php?name=Lexikon&op=content&tid=2491">computer ] [ href="module.php?name=Lexikon&op=content&tid=2545">con ] [ href="module.php?name=Lexikon&op=content&tid=2557">concurrency ] [ href="module.php?name=Lexikon&op=content&tid=2558">Concurrent C ] [ href="module.php?name=Lexikon&op=content&tid=2606">cons ] [ href="module.php?name=Lexikon&op=content&tid=2757">countable ] [ href="module.php?name=Lexikon&op=content&tid=2900">cu ] [ href="module.php?name=Lexikon&op=content&tid=2912">current ] [ href="module.php?name=Lexikon&op=content&tid=2941">cy ] [ href="module.php?name=Lexikon&op=content&tid=3151">de ] [ href="module.php?name=Lexikon&op=content&tid=3371">diff ] [ href="module.php?name=Lexikon&op=content&tid=3384">digit ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4199">et ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=4700">fo ] [ href="module.php?name=Lexikon&op=content&tid=4727">for ] [ href="module.php?name=Lexikon&op=content&tid=4828">fr ] [ href="module.php?name=Lexikon&op=content&tid=4940">function ] [ href="module.php?name=Lexikon&op=content&tid=4983">G ] [ href="module.php?name=Lexikon&op=content&tid=5057">ge ] [ href="module.php?name=Lexikon&op=content&tid=5141">gi ] [ href="module.php?name=Lexikon&op=content&tid=5291">gr ] [ href="module.php?name=Lexikon&op=content&tid=5298">grain ] [ href="module.php?name=Lexikon&op=content&tid=5403">gu ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5540">hat ] [ href="module.php?name=Lexikon&op=content&tid=5722">hose ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5791">hu ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=5956">ie ] [ href="module.php?name=Lexikon&op=content&tid=5986">iff ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6068">inc ] [ href="module.php?name=Lexikon&op=content&tid=6194">int ] [ href="module.php?name=Lexikon&op=content&tid=6413">io ] [ href="module.php?name=Lexikon&op=content&tid=6449">ir ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6789">ke ] [ href="module.php?name=Lexikon&op=content&tid=6792">ken ] [ href="module.php?name=Lexikon&op=content&tid=6918">la ] [ href="module.php?name=Lexikon&op=content&tid=6950">language ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7107">li ] [ href="module.php?name=Lexikon&op=content&tid=7399">ls ] [ href="module.php?name=Lexikon&op=content&tid=7410">lt ] [ href="module.php?name=Lexikon&op=content&tid=7415">lu ] [ href="module.php?name=Lexikon&op=content&tid=7441">ly ] [ href="module.php?name=Lexikon&op=content&tid=7457">M ] [ href="module.php?name=Lexikon&op=content&tid=7463">ma ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8167">mp ] [ href="module.php?name=Lexikon&op=content&tid=8257">Mu ] [ href="module.php?name=Lexikon&op=content&tid=8384">N ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8449">natural number ] [ href="module.php?name=Lexikon&op=content&tid=8460">nc ] [ href="module.php?name=Lexikon&op=content&tid=8472">ne ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8672">nn ] [ href="module.php?name=Lexikon&op=content&tid=8675">no ] [ href="module.php?name=Lexikon&op=content&tid=8760">ns ] [ href="module.php?name=Lexikon&op=content&tid=8787">nu ] [ href="module.php?name=Lexikon&op=content&tid=8799">numbers ] [ href="module.php?name=Lexikon&op=content&tid=8838">object ] [ href="module.php?name=Lexikon&op=content&tid=8864">object-oriented ] [ href="module.php?name=Lexikon&op=content&tid=8869">object-oriented language ] [ href="module.php?name=Lexikon&op=content&tid=8964">om ] [ href="module.php?name=Lexikon&op=content&tid=9204">pa ] [ href="module.php?name=Lexikon&op=content&tid=9457">pe ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=9651">pl ] [ href="module.php?name=Lexikon&op=content&tid=9908">pr ] [ href="module.php?name=Lexikon&op=content&tid=10079">proof ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10390">real ] [ href="module.php?name=Lexikon&op=content&tid=10396">real number ] [ href="module.php?name=Lexikon&op=content&tid=10767">ro ] [ href="module.php?name=Lexikon&op=content&tid=10918">S ] [ href="module.php?name=Lexikon&op=content&tid=10922">sa ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11259">serve ] [ href="module.php?name=Lexikon&op=content&tid=11281">set ] [ href="module.php?name=Lexikon&op=content&tid=11376">si ] [ href="module.php?name=Lexikon&op=content&tid=11651">so ] [ href="module.php?name=Lexikon&op=content&tid=11790">spec ] [ href="module.php?name=Lexikon&op=content&tid=11934">st ] [ href="module.php?name=Lexikon&op=content&tid=11990">state ] [ href="module.php?name=Lexikon&op=content&tid=12133">su ] [ href="module.php?name=Lexikon&op=content&tid=12212">surjective ] [ href="module.php?name=Lexikon&op=content&tid=12359">T ] [ href="module.php?name=Lexikon&op=content&tid=12369">table ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12721">to ] [ href="module.php?name=Lexikon&op=content&tid=12970">type ] [ href="module.php?name=Lexikon&op=content&tid=12986">ua ] [ href="module.php?name=Lexikon&op=content&tid=13008">ug ] [ href="module.php?name=Lexikon&op=content&tid=13030">um ] [ href="module.php?name=Lexikon&op=content&tid=13042">uncountable ] [ href="module.php?name=Lexikon&op=content&tid=13175">us ] [ href="module.php?name=Lexikon&op=content&tid=13252">va ] [ href="module.php?name=Lexikon&op=content&tid=13260">value ] [ href="module.php?name=Lexikon&op=content&tid=13310">ve ] [ href="module.php?name=Lexikon&op=content&tid=13366">vi ] [ href="module.php?name=Lexikon&op=content&tid=13877">ws ]
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