Truth set of this predicate

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So say I have the following predicate:



$P(x): x = x + 1$



Which is in the domain of the integers ($Z$).



Is the truth set for this predicate empty or is it:



0, 1, 2, 3, 4, 5 ...







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  • 2




    In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
    – esotechnica
    Aug 19 at 7:34











  • @esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
    – Sphero
    Aug 19 at 7:38






  • 1




    Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
    – esotechnica
    Aug 19 at 7:41











  • Okay, thanks for the help.
    – Sphero
    Aug 19 at 7:43














up vote
-1
down vote

favorite












So say I have the following predicate:



$P(x): x = x + 1$



Which is in the domain of the integers ($Z$).



Is the truth set for this predicate empty or is it:



0, 1, 2, 3, 4, 5 ...







share|cite|improve this question
















  • 2




    In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
    – esotechnica
    Aug 19 at 7:34











  • @esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
    – Sphero
    Aug 19 at 7:38






  • 1




    Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
    – esotechnica
    Aug 19 at 7:41











  • Okay, thanks for the help.
    – Sphero
    Aug 19 at 7:43












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











So say I have the following predicate:



$P(x): x = x + 1$



Which is in the domain of the integers ($Z$).



Is the truth set for this predicate empty or is it:



0, 1, 2, 3, 4, 5 ...







share|cite|improve this question












So say I have the following predicate:



$P(x): x = x + 1$



Which is in the domain of the integers ($Z$).



Is the truth set for this predicate empty or is it:



0, 1, 2, 3, 4, 5 ...









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 19 at 7:29









Sphero

147




147







  • 2




    In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
    – esotechnica
    Aug 19 at 7:34











  • @esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
    – Sphero
    Aug 19 at 7:38






  • 1




    Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
    – esotechnica
    Aug 19 at 7:41











  • Okay, thanks for the help.
    – Sphero
    Aug 19 at 7:43












  • 2




    In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
    – esotechnica
    Aug 19 at 7:34











  • @esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
    – Sphero
    Aug 19 at 7:38






  • 1




    Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
    – esotechnica
    Aug 19 at 7:41











  • Okay, thanks for the help.
    – Sphero
    Aug 19 at 7:43







2




2




In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
– esotechnica
Aug 19 at 7:34





In your situation, the predicate P is a function that maps each element of $mathbbZ$ to a truth value (true or false, T or F, 1 or 0, $top$ or $bot$, etc..). I'm not sure what a 'truth set' is, as you haven't defined it. If a truth set is the set $T = P(x)$ then yes, it is an empty set, as no integer will make this equation true.
– esotechnica
Aug 19 at 7:34













@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
– Sphero
Aug 19 at 7:38




@esotechnica The definition of a truth set is the set of all values in the domain (Z) that when assigned to x, make P(x) a true statement.
– Sphero
Aug 19 at 7:38




1




1




Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
– esotechnica
Aug 19 at 7:41





Ok, I've never heard that term, but I guessed correctly what the meaning is. I would usually call it a solution set. That is, the solution set is the empty set, because there are no solutions to this equation in $mathbbZ$
– esotechnica
Aug 19 at 7:41













Okay, thanks for the help.
– Sphero
Aug 19 at 7:43




Okay, thanks for the help.
– Sphero
Aug 19 at 7:43















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