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constructive


A proof that something exists is "constructive" if it provides a method for actually constructing it. ref="module.php?name=Lexikon&file=search&eid=1&query=Cantor">Cantor' s proof that the ref="module.php?name=Lexikon&file=search&eid=1&query=real number">real numbers are ref="module.php?name=Lexikon&file=search&eid=1&query=uncountable">uncountable can be thought of as a *non-constructive* proof that {irrational number}s exist. (There are easy constructive proofs, too but there are existence theorems with no known constructive proof). Obviously, all else being equal, constructive proofs are better than non-constructive proofs. A few mathematicians actually reject *all* non-constructive arguments as invalid this means, for instance, that the law of the {excluded middle} (either P or not-P must hold, whatever P is) has to go this makes proof by contradiction invalid. See ref="module.php?name=Lexikon&file=search&eid=1&query=intuitionistic logic">intuitionistic logic for more information on this. Most mathematicians are perfectly happy with non-constructive proofs however, the constructive approach is popular in theoretical computer science, both because computer scientists are less given to abstraction than mathematicians and because ref="module.php?name=Lexikon&file=search&eid=1&query=intuitionistic logic">intuitionistic logic turns out to be the right theory for a theoretical treatment of the foundations of computer science. (1995-04-13)

In addition suitable contents:
[ ref="module.php?name=Lexikon&op=content&tid=134">= ] [ ref="module.php?name=Lexikon&op=content&tid=178">abstraction ] [ ref="module.php?name=Lexikon&op=content&tid=262">ad ] [ ref="module.php?name=Lexikon&op=content&tid=433">al ] [ ref="module.php?name=Lexikon&op=content&tid=544">am ] [ ref="module.php?name=Lexikon&op=content&tid=592">an ] [ ref="module.php?name=Lexikon&op=content&tid=683">app ] [ ref="module.php?name=Lexikon&op=content&tid=740">ar ] [ ref="module.php?name=Lexikon&op=content&tid=743">arc ] [ ref="module.php?name=Lexikon&op=content&tid=759">arg ] [ ref="module.php?name=Lexikon&op=content&tid=760">argument ] [ ref="module.php?name=Lexikon&op=content&tid=800">as ] [ ref="module.php?name=Lexikon&op=content&tid=894">at ] [ ref="module.php?name=Lexikon&op=content&tid=935">au ] [ ref="module.php?name=Lexikon&op=content&tid=1006">aw ] [ ref="module.php?name=Lexikon&op=content&tid=1026">b ] [ ref="module.php?name=Lexikon&op=content&tid=1181">be ] [ ref="module.php?name=Lexikon&op=content&tid=1444">bo ] [ ref="module.php?name=Lexikon&op=content&tid=1501">bot ] [ ref="module.php?name=Lexikon&op=content&tid=1606">bs ] [ ref="module.php?name=Lexikon&op=content&tid=1691">bv ] [ ref="module.php?name=Lexikon&op=content&tid=1695">by ] [ ref="module.php?name=Lexikon&op=content&tid=1708">C ] [ ref="module.php?name=Lexikon&op=content&tid=1724">ca ] [ ref="module.php?name=Lexikon&op=content&tid=1807">Cantor ] [ ref="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ref="module.php?name=Lexikon&op=content&tid=2099">ci ] [ ref="module.php?name=Lexikon&op=content&tid=2138">cl ] [ ref="module.php?name=Lexikon&op=content&tid=2247">co ] [ ref="module.php?name=Lexikon&op=content&tid=2330">com ] [ ref="module.php?name=Lexikon&op=content&tid=2491">computer ] [ ref="module.php?name=Lexikon&op=content&tid=2545">con ] [ ref="module.php?name=Lexikon&op=content&tid=2606">cons ] [ ref="module.php?name=Lexikon&op=content&tid=2757">countable ] [ ref="module.php?name=Lexikon&op=content&tid=3136">dd ] [ ref="module.php?name=Lexikon&op=content&tid=3151">de ] [ ref="module.php?name=Lexikon&op=content&tid=3752">du ] [ ref="module.php?name=Lexikon&op=content&tid=3865">ec ] [ ref="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ref="module.php?name=Lexikon&op=content&tid=3929">ee ] [ ref="module.php?name=Lexikon&op=content&tid=4148">er ] [ ref="module.php?name=Lexikon&op=content&tid=4171">es ] [ ref="module.php?name=Lexikon&op=content&tid=4199">et ] [ ref="module.php?name=Lexikon&op=content&tid=4273">excl ] [ ref="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ref="module.php?name=Lexikon&op=content&tid=4520">file ] [ ref="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ref="module.php?name=Lexikon&op=content&tid=4727">for ] [ ref="module.php?name=Lexikon&op=content&tid=4801">foundation ] [ ref="module.php?name=Lexikon&op=content&tid=5134">gh ] [ ref="module.php?name=Lexikon&op=content&tid=5141">gi ] [ ref="module.php?name=Lexikon&op=content&tid=5403">gu ] [ ref="module.php?name=Lexikon&op=content&tid=5434">h ] [ ref="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ref="module.php?name=Lexikon&op=content&tid=5656">hing ] [ ref="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ref="module.php?name=Lexikon&op=content&tid=5779">ht ] [ ref="module.php?name=Lexikon&op=content&tid=5931">id ] [ ref="module.php?name=Lexikon&op=content&tid=5956">ie ] [ ref="module.php?name=Lexikon&op=content&tid=6013">il ] [ ref="module.php?name=Lexikon&op=content&tid=6064">in ] [ ref="module.php?name=Lexikon&op=content&tid=6179">instance ] [ ref="module.php?name=Lexikon&op=content&tid=6194">int ] [ ref="module.php?name=Lexikon&op=content&tid=6403">intuitionistic logic ] [ ref="module.php?name=Lexikon&op=content&tid=6413">io ] [ ref="module.php?name=Lexikon&op=content&tid=6449">ir ] [ ref="module.php?name=Lexikon&op=content&tid=6474">irrational number ] [ ref="module.php?name=Lexikon&op=content&tid=6482">is ] [ ref="module.php?name=Lexikon&op=content&tid=6558">it ] [ ref="module.php?name=Lexikon&op=content&tid=6789">ke ] [ ref="module.php?name=Lexikon&op=content&tid=6861">kn ] [ ref="module.php?name=Lexikon&op=content&tid=6918">la ] [ ref="module.php?name=Lexikon&op=content&tid=6996">law ] [ ref="module.php?name=Lexikon&op=content&tid=7023">ld ] [ ref="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ref="module.php?name=Lexikon&op=content&tid=7107">li ] [ ref="module.php?name=Lexikon&op=content&tid=7399">ls ] [ ref="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ref="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ref="module.php?name=Lexikon&op=content&tid=7457">M ] [ ref="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ref="module.php?name=Lexikon&op=content&tid=7817">method ] [ ref="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ref="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ref="module.php?name=Lexikon&op=content&tid=8079">module ] [ ref="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ref="module.php?name=Lexikon&op=content&tid=8228">ms ] [ ref="module.php?name=Lexikon&op=content&tid=8258">mu ] [ ref="module.php?name=Lexikon&op=content&tid=8386">na ] [ ref="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ref="module.php?name=Lexikon&op=content&tid=8622">nf ] [ ref="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ref="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ref="module.php?name=Lexikon&op=content&tid=8675">no ] [ ref="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ref="module.php?name=Lexikon&op=content&tid=8787">nu ] [ ref="module.php?name=Lexikon&op=content&tid=8820">O ] [ ref="module.php?name=Lexikon&op=content&tid=8964">om ] [ ref="module.php?name=Lexikon&op=content&tid=9014">op ] [ ref="module.php?name=Lexikon&op=content&tid=9457">pe ] [ ref="module.php?name=Lexikon&op=content&tid=9494">perf ] [ ref="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ref="module.php?name=Lexikon&op=content&tid=9801">pop ] [ ref="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ref="module.php?name=Lexikon&op=content&tid=10079">proof ] [ ref="module.php?name=Lexikon&op=content&tid=10194">py ] [ ref="module.php?name=Lexikon&op=content&tid=10253">query ] [ ref="module.php?name=Lexikon&op=content&tid=10348">rational ] [ ref="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ref="module.php?name=Lexikon&op=content&tid=10385">re ] [ ref="module.php?name=Lexikon&op=content&tid=10390">real ] [ ref="module.php?name=Lexikon&op=content&tid=10396">real number ] [ ref="module.php?name=Lexikon&op=content&tid=10767">ro ] [ ref="module.php?name=Lexikon&op=content&tid=10768">roach ] [ ref="module.php?name=Lexikon&op=content&tid=10887">ru ] [ ref="module.php?name=Lexikon&op=content&tid=10918">S ] [ ref="module.php?name=Lexikon&op=content&tid=11010">sc ] [ ref="module.php?name=Lexikon&op=content&tid=11150">se ] [ ref="module.php?name=Lexikon&op=content&tid=11525">sl ] [ ref="module.php?name=Lexikon&op=content&tid=11651">so ] [ ref="module.php?name=Lexikon&op=content&tid=11934">st ] [ ref="module.php?name=Lexikon&op=content&tid=12109">struct ] [ ref="module.php?name=Lexikon&op=content&tid=12246">sy ] [ ref="module.php?name=Lexikon&op=content&tid=12359">T ] [ ref="module.php?name=Lexikon&op=content&tid=12369">table ] [ ref="module.php?name=Lexikon&op=content&tid=12588">th ] [ ref="module.php?name=Lexikon&op=content&tid=12602">theory ] [ ref="module.php?name=Lexikon&op=content&tid=12708">tm ] [ ref="module.php?name=Lexikon&op=content&tid=12721">to ] [ ref="module.php?name=Lexikon&op=content&tid=12787">tr ] [ ref="module.php?name=Lexikon&op=content&tid=12896">tt ] [ ref="module.php?name=Lexikon&op=content&tid=12986">ua ] [ ref="module.php?name=Lexikon&op=content&tid=13008">ug ] [ ref="module.php?name=Lexikon&op=content&tid=13030">um ] [ ref="module.php?name=Lexikon&op=content&tid=13042">uncountable ] [ ref="module.php?name=Lexikon&op=content&tid=13175">us ] [ ref="module.php?name=Lexikon&op=content&tid=13252">va ] [ ref="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ref="module.php?name=Lexikon&op=content&tid=13366">vi ]






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