MyWikiBiz, Author Your Legacy — Monday July 01, 2024
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, 20:00, 3 May 2012
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− | <pre>
| + | Finally, the reflectively extended naming function <math>\operatorname{Nom}' : O' \to S'\!</math> is defined as <math>\operatorname{Nom}' = \operatorname{Nom} \cup Nom_1.\!</math> |
− | Finally, the reflectively extended naming function Nom' : O' > S' is defined as Nom' = Nom U Nom'. | |
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| A few remarks are necessary to see how this way of defining a CRE can be regarded as legitimate. | | A few remarks are necessary to see how this way of defining a CRE can be regarded as legitimate. |
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− | In the present context an application of the arch notation "<x>" is read on analogy with the use of any other functional notation "f(x)", where "f" is the name of a function f, "f( )" is the context of its application, "x" is the name of an argument x, and where the functional abstraction "x > f(x)" is just another name for the function f. | + | In the present context an application of the arch notation, for example, <math>{}^{\langle} x {}^{\rangle},\!</math> is read on analogy with the use of any other functional notation, for example, <math>f(x),\!</math> where <math>{}^{\backprime\backprime} f {}^{\prime\prime}\!</math> is the name of a function <math>f,\!</math> <math>{}^{\backprime\backprime} f(~) {}^{\prime\prime}\!</math> is the context of its application, <math>{}^{\backprime\backprime} x {}^{\prime\prime}\!</math> is the name of an argument <math>x,\!</math> and where the functional abstraction <math>{}^{\backprime\backprime} x \mapsto f(x) {}^{\prime\prime}\!</math> is just another name for the function <math>f.\!</math> |
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| + | <pre> |
| It is clear that some form of functional abstraction is being invoked in the definition of Nom1, above. Otherwise, the expression "x > <x>" would indicate a constant function, one that maps every x in its domain to the same sign or code for the letter "x". But if this is allowed, then it seems either to invoke a more powerful concept, lambda abstraction, than the one being defined or else to attempt an improper definition of the naming function in terms of itself. | | It is clear that some form of functional abstraction is being invoked in the definition of Nom1, above. Otherwise, the expression "x > <x>" would indicate a constant function, one that maps every x in its domain to the same sign or code for the letter "x". But if this is allowed, then it seems either to invoke a more powerful concept, lambda abstraction, than the one being defined or else to attempt an improper definition of the naming function in terms of itself. |
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