Can a colon be used in predicate logic?
$begingroup$
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
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
asked Dec 19 '18 at 14:28
Taran BasiTaran Basi
6
$endgroup$
add a comment |
$begingroup$
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
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
asked Dec 19 '18 at 14:28
Taran BasiTaran Basi
6
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
asked Dec 19 '18 at 14:28
Taran BasiTaran Basi
6
$endgroup$
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
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
asked Dec 19 '18 at 14:28
Taran BasiTaran Basi
6
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
asked Dec 19 '18 at 14:28
Taran BasiTaran Basi
6
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
edited Dec 19 '18 at 14:34
Christoph
12.5k1642
12.5k1642
asked Dec 19 '18 at 14:28
Taran BasiTaran Basi
6
asked Dec 19 '18 at 14:28
Taran BasiTaran Basi
6
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
add a comment |
$begingroup$
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
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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.
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
$endgroup$
add a comment |
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1 Answer
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1 Answer
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votes
$begingroup$
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.
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
$endgroup$
add a comment |
$begingroup$
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.
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
$endgroup$
add a comment |
$begingroup$
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.
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
$endgroup$
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.
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
answered Dec 19 '18 at 14:44
Theo BenditTheo Bendit
19.6k12354
19.6k12354
add a comment |
add a comment |
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$begingroup$
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