Can a colon be used in predicate logic?












0












$begingroup$


Is a colon or letter $e$ used to describe if something (lets say $x$) is an element or part of something? What's the correct way to write it out?? My lecturer showed us to write it using a colon but another video on YouTube showed me to use the letter $e$.



For example, is it:




$exists x:S, neg ( (D(x) wedge c(x) )$




or:




$exists xeS, neg ( (D(x) wedge c(x) )$




Thanks!






notation predicate-logic







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$endgroup$












  • $begingroup$
    Is not the letter "e"; it is the membership relation : $in$. $exists x in S [D(x) land C(x)]$.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 14:31












  • $begingroup$
    So I use '∈' and not ':' ?
    $endgroup$
    – Taran Basi
    Dec 19 '18 at 14:33
















0












$begingroup$


Is a colon or letter $e$ used to describe if something (lets say $x$) is an element or part of something? What's the correct way to write it out?? My lecturer showed us to write it using a colon but another video on YouTube showed me to use the letter $e$.



For example, is it:




$exists x:S, neg ( (D(x) wedge c(x) )$




or:




$exists xeS, neg ( (D(x) wedge c(x) )$




Thanks!






notation predicate-logic







share|cite|improve this question











$endgroup$












  • $begingroup$
    Is not the letter "e"; it is the membership relation : $in$. $exists x in S [D(x) land C(x)]$.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 14:31












  • $begingroup$
    So I use '∈' and not ':' ?
    $endgroup$
    – Taran Basi
    Dec 19 '18 at 14:33














0












0








0





$begingroup$


Is a colon or letter $e$ used to describe if something (lets say $x$) is an element or part of something? What's the correct way to write it out?? My lecturer showed us to write it using a colon but another video on YouTube showed me to use the letter $e$.



For example, is it:




$exists x:S, neg ( (D(x) wedge c(x) )$




or:




$exists xeS, neg ( (D(x) wedge c(x) )$




Thanks!






notation predicate-logic







share|cite|improve this question











$endgroup$




Is a colon or letter $e$ used to describe if something (lets say $x$) is an element or part of something? What's the correct way to write it out?? My lecturer showed us to write it using a colon but another video on YouTube showed me to use the letter $e$.



For example, is it:




$exists x:S, neg ( (D(x) wedge c(x) )$




or:




$exists xeS, neg ( (D(x) wedge c(x) )$




Thanks!






notation predicate-logic




notation predicate-logic






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 19 '18 at 14:34









Christoph

12.5k1642




12.5k1642










asked Dec 19 '18 at 14:28









Taran BasiTaran Basi

6




6












  • $begingroup$
    Is not the letter "e"; it is the membership relation : $in$. $exists x in S [D(x) land C(x)]$.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 14:31












  • $begingroup$
    So I use '∈' and not ':' ?
    $endgroup$
    – Taran Basi
    Dec 19 '18 at 14:33


















  • $begingroup$
    Is not the letter "e"; it is the membership relation : $in$. $exists x in S [D(x) land C(x)]$.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 14:31












  • $begingroup$
    So I use '∈' and not ':' ?
    $endgroup$
    – Taran Basi
    Dec 19 '18 at 14:33
















$begingroup$
Is not the letter "e"; it is the membership relation : $in$. $exists x in S [D(x) land C(x)]$.
$endgroup$
– Mauro ALLEGRANZA
Dec 19 '18 at 14:31






$begingroup$
Is not the letter "e"; it is the membership relation : $in$. $exists x in S [D(x) land C(x)]$.
$endgroup$
– Mauro ALLEGRANZA
Dec 19 '18 at 14:31














$begingroup$
So I use '∈' and not ':' ?
$endgroup$
– Taran Basi
Dec 19 '18 at 14:33




$begingroup$
So I use '∈' and not ':' ?
$endgroup$
– Taran Basi
Dec 19 '18 at 14:33










1 Answer
1






active

oldest

votes


















1












$begingroup$

The little 'e' is non-standard. It's sometimes used as a poor substitute for the "element of" relation $in$, when typing mathematics without Latex (or extended characters). I cannot overstate how shoddy this is considered to be; never, under any other circumstances, use it in lieu of $in$ (and even in those circumstances, I would do everything in my power, including typing the words "is an element of", to avoid using 'e' to replace $in$). Certainly, when you're writing by hand, or on this site, you should use the $in$ character. It can be accessed through Latex/MathJax by typing in.



The colon is something different. It usually stands for "such that". You could write,
$$forall x in mathbb{R}, exists y in mathbb{R} : x + y = 0,$$
which reads,




For all $x$ in the set $mathbb{R}$, there exists a $y$ in the set $mathbb{R}$ such that $x + y = 0$.




It's not about something being an element of something else, it's a symbol short for the phrase "such that". Formally, it's not really a necessary phrase; it arguably makes the logical symbols a bit more readable. You may, if you wish, omit the comma and colon, and write
$$(forall x in mathbb{R})(exists y in mathbb{R})(x + y = 0).$$
It means the same thing.






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    $begingroup$

    The little 'e' is non-standard. It's sometimes used as a poor substitute for the "element of" relation $in$, when typing mathematics without Latex (or extended characters). I cannot overstate how shoddy this is considered to be; never, under any other circumstances, use it in lieu of $in$ (and even in those circumstances, I would do everything in my power, including typing the words "is an element of", to avoid using 'e' to replace $in$). Certainly, when you're writing by hand, or on this site, you should use the $in$ character. It can be accessed through Latex/MathJax by typing in.



    The colon is something different. It usually stands for "such that". You could write,
    $$forall x in mathbb{R}, exists y in mathbb{R} : x + y = 0,$$
    which reads,




    For all $x$ in the set $mathbb{R}$, there exists a $y$ in the set $mathbb{R}$ such that $x + y = 0$.




    It's not about something being an element of something else, it's a symbol short for the phrase "such that". Formally, it's not really a necessary phrase; it arguably makes the logical symbols a bit more readable. You may, if you wish, omit the comma and colon, and write
    $$(forall x in mathbb{R})(exists y in mathbb{R})(x + y = 0).$$
    It means the same thing.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      The little 'e' is non-standard. It's sometimes used as a poor substitute for the "element of" relation $in$, when typing mathematics without Latex (or extended characters). I cannot overstate how shoddy this is considered to be; never, under any other circumstances, use it in lieu of $in$ (and even in those circumstances, I would do everything in my power, including typing the words "is an element of", to avoid using 'e' to replace $in$). Certainly, when you're writing by hand, or on this site, you should use the $in$ character. It can be accessed through Latex/MathJax by typing in.



      The colon is something different. It usually stands for "such that". You could write,
      $$forall x in mathbb{R}, exists y in mathbb{R} : x + y = 0,$$
      which reads,




      For all $x$ in the set $mathbb{R}$, there exists a $y$ in the set $mathbb{R}$ such that $x + y = 0$.




      It's not about something being an element of something else, it's a symbol short for the phrase "such that". Formally, it's not really a necessary phrase; it arguably makes the logical symbols a bit more readable. You may, if you wish, omit the comma and colon, and write
      $$(forall x in mathbb{R})(exists y in mathbb{R})(x + y = 0).$$
      It means the same thing.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        The little 'e' is non-standard. It's sometimes used as a poor substitute for the "element of" relation $in$, when typing mathematics without Latex (or extended characters). I cannot overstate how shoddy this is considered to be; never, under any other circumstances, use it in lieu of $in$ (and even in those circumstances, I would do everything in my power, including typing the words "is an element of", to avoid using 'e' to replace $in$). Certainly, when you're writing by hand, or on this site, you should use the $in$ character. It can be accessed through Latex/MathJax by typing in.



        The colon is something different. It usually stands for "such that". You could write,
        $$forall x in mathbb{R}, exists y in mathbb{R} : x + y = 0,$$
        which reads,




        For all $x$ in the set $mathbb{R}$, there exists a $y$ in the set $mathbb{R}$ such that $x + y = 0$.




        It's not about something being an element of something else, it's a symbol short for the phrase "such that". Formally, it's not really a necessary phrase; it arguably makes the logical symbols a bit more readable. You may, if you wish, omit the comma and colon, and write
        $$(forall x in mathbb{R})(exists y in mathbb{R})(x + y = 0).$$
        It means the same thing.






        share|cite|improve this answer









        $endgroup$



        The little 'e' is non-standard. It's sometimes used as a poor substitute for the "element of" relation $in$, when typing mathematics without Latex (or extended characters). I cannot overstate how shoddy this is considered to be; never, under any other circumstances, use it in lieu of $in$ (and even in those circumstances, I would do everything in my power, including typing the words "is an element of", to avoid using 'e' to replace $in$). Certainly, when you're writing by hand, or on this site, you should use the $in$ character. It can be accessed through Latex/MathJax by typing in.



        The colon is something different. It usually stands for "such that". You could write,
        $$forall x in mathbb{R}, exists y in mathbb{R} : x + y = 0,$$
        which reads,




        For all $x$ in the set $mathbb{R}$, there exists a $y$ in the set $mathbb{R}$ such that $x + y = 0$.




        It's not about something being an element of something else, it's a symbol short for the phrase "such that". Formally, it's not really a necessary phrase; it arguably makes the logical symbols a bit more readable. You may, if you wish, omit the comma and colon, and write
        $$(forall x in mathbb{R})(exists y in mathbb{R})(x + y = 0).$$
        It means the same thing.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 19 '18 at 14:44









        Theo BenditTheo Bendit

        19.6k12354




        19.6k12354






























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