| dbo:description
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- rezultat, ki dokazuje, da določenega problema ni mogoče rešiti, kot je opisano v trditvi, ali da določenega sklopa problemov ni mogoče rešiti na splošno (sl)
- demostración de que un postulado no es verdadero (es decir, no puede cumplirse) (es)
- result demonstrating that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general (en)
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| dbp:text
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- Richard's paradox ... is as follows. Consider all decimals that can be defined by means of a finite number of words ([“words” are symbols; boldface added for emphasis]); let E be the class of such decimals. Then E has ([an infinite number of]) terms; hence its members can be ordered as the 1st, 2nd, 3rd, ... Let X be a number defined as follows ([Whitehead & Russell now employ the Cantor diagonal method]). (en)
- If the n-th figure in the n-th decimal is p, let the n-th figure in X be p + 1 . Then X is different from all the members of E, since, whatever finite value n may have, the n-th figure in X is different from the n-th figure in the n-th of the decimals composing E, and therefore X is different from the n-th decimal. Nevertheless we have defined X in a finite number of words ([i.e. this very definition of “word” above.]) and therefore X ought to be a member of E. Thus X both is and is not a member of E. (en)
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