What is uniqueness quantification?
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Can someone explain the concept of Uniqueness quantification ∃! in an easily understandable way since I can't understand the definition of it, what's special about it with other logical operators like and, or, not?
*
discrete-mathematics logic definition
asked Dec 9 '18 at 5:20
CColaCCola
346
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add a comment |
$begingroup$
Can someone explain the concept of Uniqueness quantification ∃! in an easily understandable way since I can't understand the definition of it, what's special about it with other logical operators like and, or, not?
*
discrete-mathematics logic definition
asked Dec 9 '18 at 5:20
CColaCCola
346
$endgroup$
3
$begingroup$
I do not know what the uniqueness operator is... I don't think it's a standard term. (Do you mean the unique existential quantifier as in $exists ! xphi(x)$?) Maybe write down the definition and give a little more context?
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– spaceisdarkgreen
Dec 9 '18 at 5:24
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thank you I corrected the typo mistake
$endgroup$
– CCola
Dec 9 '18 at 6:18
add a comment |
$begingroup$
Can someone explain the concept of Uniqueness quantification ∃! in an easily understandable way since I can't understand the definition of it, what's special about it with other logical operators like and, or, not?
*
discrete-mathematics logic definition
asked Dec 9 '18 at 5:20
CColaCCola
346
$endgroup$
Can someone explain the concept of Uniqueness quantification ∃! in an easily understandable way since I can't understand the definition of it, what's special about it with other logical operators like and, or, not?
*
discrete-mathematics logic definition
discrete-mathematics logic definition
asked Dec 9 '18 at 5:20
CColaCCola
346
asked Dec 9 '18 at 5:20
CColaCCola
346
edited Dec 9 '18 at 6:17
CCola
asked Dec 9 '18 at 5:20
CColaCCola
346
asked Dec 9 '18 at 5:20
CColaCCola
346
asked Dec 9 '18 at 5:20
CColaCCola
346
346
3
$begingroup$
I do not know what the uniqueness operator is... I don't think it's a standard term. (Do you mean the unique existential quantifier as in $exists ! xphi(x)$?) Maybe write down the definition and give a little more context?
$endgroup$
– spaceisdarkgreen
Dec 9 '18 at 5:24
$begingroup$
thank you I corrected the typo mistake
$endgroup$
– CCola
Dec 9 '18 at 6:18
add a comment |
3
$begingroup$
I do not know what the uniqueness operator is... I don't think it's a standard term. (Do you mean the unique existential quantifier as in $exists ! xphi(x)$?) Maybe write down the definition and give a little more context?
$endgroup$
– spaceisdarkgreen
Dec 9 '18 at 5:24
$begingroup$
thank you I corrected the typo mistake
$endgroup$
– CCola
Dec 9 '18 at 6:18
3
3
$begingroup$
I do not know what the uniqueness operator is... I don't think it's a standard term. (Do you mean the unique existential quantifier as in $exists ! xphi(x)$?) Maybe write down the definition and give a little more context?
$endgroup$
– spaceisdarkgreen
Dec 9 '18 at 5:24
$begingroup$
I do not know what the uniqueness operator is... I don't think it's a standard term. (Do you mean the unique existential quantifier as in $exists ! xphi(x)$?) Maybe write down the definition and give a little more context?
$endgroup$
– spaceisdarkgreen
Dec 9 '18 at 5:24
$begingroup$
thank you I corrected the typo mistake
$endgroup$
– CCola
Dec 9 '18 at 6:18
$begingroup$
thank you I corrected the typo mistake
$endgroup$
– CCola
Dec 9 '18 at 6:18
add a comment |
1 Answer
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I think the "Uniqueness quantification" Wikipedia article does a fair job of answering this question, but try this: how many integers are there which, when added to $3$ give you $7$? Only one, namely $4$. But how many integers are there which, when squared give you $25$? Two! ($5$ and $-5$.)
The uniqueness operator is a mathematical convention which allows us to describe the phenomenon which occurs when there is one and only one mathematical object which satisfies the given conditions.
In practice, you will usually see it paired with the existence operator "$exists$". This might look like the following: $forall x in mathbb{Z}$, $exists ! y in mathbb{Z}$ such that $x+y=0$. Translation: "For every integer $x$, there exists a unique integer $y$ such that $x+y=0$ (This is the additive inverse property).
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
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$begingroup$
Please edit this answer to include a link to the Wikipedia article you mentioned.
$endgroup$
– Shaun
Dec 9 '18 at 6:06
add a comment |
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1 Answer
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$begingroup$
I think the "Uniqueness quantification" Wikipedia article does a fair job of answering this question, but try this: how many integers are there which, when added to $3$ give you $7$? Only one, namely $4$. But how many integers are there which, when squared give you $25$? Two! ($5$ and $-5$.)
The uniqueness operator is a mathematical convention which allows us to describe the phenomenon which occurs when there is one and only one mathematical object which satisfies the given conditions.
In practice, you will usually see it paired with the existence operator "$exists$". This might look like the following: $forall x in mathbb{Z}$, $exists ! y in mathbb{Z}$ such that $x+y=0$. Translation: "For every integer $x$, there exists a unique integer $y$ such that $x+y=0$ (This is the additive inverse property).
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
$endgroup$
$begingroup$
Please edit this answer to include a link to the Wikipedia article you mentioned.
$endgroup$
– Shaun
Dec 9 '18 at 6:06
add a comment |
$begingroup$
I think the "Uniqueness quantification" Wikipedia article does a fair job of answering this question, but try this: how many integers are there which, when added to $3$ give you $7$? Only one, namely $4$. But how many integers are there which, when squared give you $25$? Two! ($5$ and $-5$.)
The uniqueness operator is a mathematical convention which allows us to describe the phenomenon which occurs when there is one and only one mathematical object which satisfies the given conditions.
In practice, you will usually see it paired with the existence operator "$exists$". This might look like the following: $forall x in mathbb{Z}$, $exists ! y in mathbb{Z}$ such that $x+y=0$. Translation: "For every integer $x$, there exists a unique integer $y$ such that $x+y=0$ (This is the additive inverse property).
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
$endgroup$
$begingroup$
Please edit this answer to include a link to the Wikipedia article you mentioned.
$endgroup$
– Shaun
Dec 9 '18 at 6:06
add a comment |
$begingroup$
I think the "Uniqueness quantification" Wikipedia article does a fair job of answering this question, but try this: how many integers are there which, when added to $3$ give you $7$? Only one, namely $4$. But how many integers are there which, when squared give you $25$? Two! ($5$ and $-5$.)
The uniqueness operator is a mathematical convention which allows us to describe the phenomenon which occurs when there is one and only one mathematical object which satisfies the given conditions.
In practice, you will usually see it paired with the existence operator "$exists$". This might look like the following: $forall x in mathbb{Z}$, $exists ! y in mathbb{Z}$ such that $x+y=0$. Translation: "For every integer $x$, there exists a unique integer $y$ such that $x+y=0$ (This is the additive inverse property).
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
$endgroup$
I think the "Uniqueness quantification" Wikipedia article does a fair job of answering this question, but try this: how many integers are there which, when added to $3$ give you $7$? Only one, namely $4$. But how many integers are there which, when squared give you $25$? Two! ($5$ and $-5$.)
The uniqueness operator is a mathematical convention which allows us to describe the phenomenon which occurs when there is one and only one mathematical object which satisfies the given conditions.
In practice, you will usually see it paired with the existence operator "$exists$". This might look like the following: $forall x in mathbb{Z}$, $exists ! y in mathbb{Z}$ such that $x+y=0$. Translation: "For every integer $x$, there exists a unique integer $y$ such that $x+y=0$ (This is the additive inverse property).
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
edited Dec 9 '18 at 8:01
Raymond Hettinger
46119
46119
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
answered Dec 9 '18 at 5:33
Adam CartisanoAdam Cartisano
1764
1764
$begingroup$
Please edit this answer to include a link to the Wikipedia article you mentioned.
$endgroup$
– Shaun
Dec 9 '18 at 6:06
add a comment |
$begingroup$
Please edit this answer to include a link to the Wikipedia article you mentioned.
$endgroup$
– Shaun
Dec 9 '18 at 6:06
$begingroup$
Please edit this answer to include a link to the Wikipedia article you mentioned.
$endgroup$
– Shaun
Dec 9 '18 at 6:06
$begingroup$
Please edit this answer to include a link to the Wikipedia article you mentioned.
$endgroup$
– Shaun
Dec 9 '18 at 6:06
add a comment |
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3
$begingroup$
I do not know what the uniqueness operator is... I don't think it's a standard term. (Do you mean the unique existential quantifier as in $exists ! xphi(x)$?) Maybe write down the definition and give a little more context?
$endgroup$
– spaceisdarkgreen
Dec 9 '18 at 5:24
$begingroup$
thank you I corrected the typo mistake
$endgroup$
– CCola
Dec 9 '18 at 6:18