Classification of zero polynomial [closed]
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Zero polynomial is a univariate or multivariate polynomial or this classification is not defined for it?
polynomials
asked Dec 29 '18 at 14:49
user629353user629353
1147
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closed as off-topic by amWhy, Claude Leibovici, Henrik, metamorphy, Shailesh Dec 29 '18 at 16:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Claude Leibovici, Henrik, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Zero polynomial is a univariate or multivariate polynomial or this classification is not defined for it?
polynomials
asked Dec 29 '18 at 14:49
user629353user629353
1147
$endgroup$
closed as off-topic by amWhy, Claude Leibovici, Henrik, metamorphy, Shailesh Dec 29 '18 at 16:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Claude Leibovici, Henrik, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
3
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Is the empty set a set of integers or a set of polygons?
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– MJD
Dec 29 '18 at 14:52
$begingroup$
Belongs to neither
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– user629353
Dec 29 '18 at 14:54
$begingroup$
So is it to conclude zero polynomial doesn't fit for this classification?
$endgroup$
– user629353
Dec 29 '18 at 14:58
$begingroup$
The symbol 0 is overloaded. Sometimes it refers to the number zero, sometimes it refers to the zero polynomial in $mathbb R[x]$, sometimes it refers to the zero polynomial in $mathbb R[x,y]$, etc. Hopefully the meaning is always clear from context
$endgroup$
– littleO
Dec 29 '18 at 15:01
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So why not its better to regard it not define
$endgroup$
– user629353
Dec 29 '18 at 15:05
add a comment |
$begingroup$
Zero polynomial is a univariate or multivariate polynomial or this classification is not defined for it?
polynomials
asked Dec 29 '18 at 14:49
user629353user629353
1147
$endgroup$
Zero polynomial is a univariate or multivariate polynomial or this classification is not defined for it?
polynomials
polynomials
asked Dec 29 '18 at 14:49
user629353user629353
1147
asked Dec 29 '18 at 14:49
user629353user629353
1147
asked Dec 29 '18 at 14:49
user629353user629353
1147
asked Dec 29 '18 at 14:49
user629353user629353
1147
asked Dec 29 '18 at 14:49
user629353user629353
1147
1147
closed as off-topic by amWhy, Claude Leibovici, Henrik, metamorphy, Shailesh Dec 29 '18 at 16:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Claude Leibovici, Henrik, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by amWhy, Claude Leibovici, Henrik, metamorphy, Shailesh Dec 29 '18 at 16:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Claude Leibovici, Henrik, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
3
$begingroup$
Is the empty set a set of integers or a set of polygons?
$endgroup$
– MJD
Dec 29 '18 at 14:52
$begingroup$
Belongs to neither
$endgroup$
– user629353
Dec 29 '18 at 14:54
$begingroup$
So is it to conclude zero polynomial doesn't fit for this classification?
$endgroup$
– user629353
Dec 29 '18 at 14:58
$begingroup$
The symbol 0 is overloaded. Sometimes it refers to the number zero, sometimes it refers to the zero polynomial in $mathbb R[x]$, sometimes it refers to the zero polynomial in $mathbb R[x,y]$, etc. Hopefully the meaning is always clear from context
$endgroup$
– littleO
Dec 29 '18 at 15:01
$begingroup$
So why not its better to regard it not define
$endgroup$
– user629353
Dec 29 '18 at 15:05
add a comment |
3
$begingroup$
Is the empty set a set of integers or a set of polygons?
$endgroup$
– MJD
Dec 29 '18 at 14:52
$begingroup$
Belongs to neither
$endgroup$
– user629353
Dec 29 '18 at 14:54
$begingroup$
So is it to conclude zero polynomial doesn't fit for this classification?
$endgroup$
– user629353
Dec 29 '18 at 14:58
$begingroup$
The symbol 0 is overloaded. Sometimes it refers to the number zero, sometimes it refers to the zero polynomial in $mathbb R[x]$, sometimes it refers to the zero polynomial in $mathbb R[x,y]$, etc. Hopefully the meaning is always clear from context
$endgroup$
– littleO
Dec 29 '18 at 15:01
$begingroup$
So why not its better to regard it not define
$endgroup$
– user629353
Dec 29 '18 at 15:05
3
3
$begingroup$
Is the empty set a set of integers or a set of polygons?
$endgroup$
– MJD
Dec 29 '18 at 14:52
$begingroup$
Is the empty set a set of integers or a set of polygons?
$endgroup$
– MJD
Dec 29 '18 at 14:52
$begingroup$
Belongs to neither
$endgroup$
– user629353
Dec 29 '18 at 14:54
$begingroup$
Belongs to neither
$endgroup$
– user629353
Dec 29 '18 at 14:54
$begingroup$
So is it to conclude zero polynomial doesn't fit for this classification?
$endgroup$
– user629353
Dec 29 '18 at 14:58
$begingroup$
So is it to conclude zero polynomial doesn't fit for this classification?
$endgroup$
– user629353
Dec 29 '18 at 14:58
$begingroup$
The symbol 0 is overloaded. Sometimes it refers to the number zero, sometimes it refers to the zero polynomial in $mathbb R[x]$, sometimes it refers to the zero polynomial in $mathbb R[x,y]$, etc. Hopefully the meaning is always clear from context
$endgroup$
– littleO
Dec 29 '18 at 15:01
$begingroup$
The symbol 0 is overloaded. Sometimes it refers to the number zero, sometimes it refers to the zero polynomial in $mathbb R[x]$, sometimes it refers to the zero polynomial in $mathbb R[x,y]$, etc. Hopefully the meaning is always clear from context
$endgroup$
– littleO
Dec 29 '18 at 15:01
$begingroup$
So why not its better to regard it not define
$endgroup$
– user629353
Dec 29 '18 at 15:05
$begingroup$
So why not its better to regard it not define
$endgroup$
– user629353
Dec 29 '18 at 15:05
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The symbol $0$ can signify many things. It could mean the natural number $0$, or the real number $0$, or the zero function $Bbb RtoBbb R$, or the zero polynomial in the ring of complex polynomials in the three variables $x,y,z$. And many, many others.
Technically all these $0$'s are different. But their properties are so similar (even in the possible interactions between the algebraic structures mentioned above) that I don't know a single person who makes that difference explicit.
It does have some merit in specific problems and exercises. But then it's mostly because of how it helps the mental bookkeeping and not because of philosophical qualms with this abuse of notation.
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
$endgroup$
$begingroup$
Such bookkeeping concerns also lead to some slightly odd looking definitions, for example the best way to define the degree of the zero polynomial seems to be $-1$.
$endgroup$
– Ian
Dec 29 '18 at 15:09
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@Ian Or $-infty$, depending on which property of degree you want to preserve.
$endgroup$
– Arthur
Dec 29 '18 at 15:27
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The symbol $0$ can signify many things. It could mean the natural number $0$, or the real number $0$, or the zero function $Bbb RtoBbb R$, or the zero polynomial in the ring of complex polynomials in the three variables $x,y,z$. And many, many others.
Technically all these $0$'s are different. But their properties are so similar (even in the possible interactions between the algebraic structures mentioned above) that I don't know a single person who makes that difference explicit.
It does have some merit in specific problems and exercises. But then it's mostly because of how it helps the mental bookkeeping and not because of philosophical qualms with this abuse of notation.
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
$endgroup$
$begingroup$
Such bookkeeping concerns also lead to some slightly odd looking definitions, for example the best way to define the degree of the zero polynomial seems to be $-1$.
$endgroup$
– Ian
Dec 29 '18 at 15:09
$begingroup$
@Ian Or $-infty$, depending on which property of degree you want to preserve.
$endgroup$
– Arthur
Dec 29 '18 at 15:27
add a comment |
$begingroup$
The symbol $0$ can signify many things. It could mean the natural number $0$, or the real number $0$, or the zero function $Bbb RtoBbb R$, or the zero polynomial in the ring of complex polynomials in the three variables $x,y,z$. And many, many others.
Technically all these $0$'s are different. But their properties are so similar (even in the possible interactions between the algebraic structures mentioned above) that I don't know a single person who makes that difference explicit.
It does have some merit in specific problems and exercises. But then it's mostly because of how it helps the mental bookkeeping and not because of philosophical qualms with this abuse of notation.
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
$endgroup$
$begingroup$
Such bookkeeping concerns also lead to some slightly odd looking definitions, for example the best way to define the degree of the zero polynomial seems to be $-1$.
$endgroup$
– Ian
Dec 29 '18 at 15:09
$begingroup$
@Ian Or $-infty$, depending on which property of degree you want to preserve.
$endgroup$
– Arthur
Dec 29 '18 at 15:27
add a comment |
$begingroup$
The symbol $0$ can signify many things. It could mean the natural number $0$, or the real number $0$, or the zero function $Bbb RtoBbb R$, or the zero polynomial in the ring of complex polynomials in the three variables $x,y,z$. And many, many others.
Technically all these $0$'s are different. But their properties are so similar (even in the possible interactions between the algebraic structures mentioned above) that I don't know a single person who makes that difference explicit.
It does have some merit in specific problems and exercises. But then it's mostly because of how it helps the mental bookkeeping and not because of philosophical qualms with this abuse of notation.
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
$endgroup$
The symbol $0$ can signify many things. It could mean the natural number $0$, or the real number $0$, or the zero function $Bbb RtoBbb R$, or the zero polynomial in the ring of complex polynomials in the three variables $x,y,z$. And many, many others.
Technically all these $0$'s are different. But their properties are so similar (even in the possible interactions between the algebraic structures mentioned above) that I don't know a single person who makes that difference explicit.
It does have some merit in specific problems and exercises. But then it's mostly because of how it helps the mental bookkeeping and not because of philosophical qualms with this abuse of notation.
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
edited Dec 29 '18 at 15:02
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
answered Dec 29 '18 at 14:56
ArthurArthur
112k7107190
112k7107190
$begingroup$
Such bookkeeping concerns also lead to some slightly odd looking definitions, for example the best way to define the degree of the zero polynomial seems to be $-1$.
$endgroup$
– Ian
Dec 29 '18 at 15:09
$begingroup$
@Ian Or $-infty$, depending on which property of degree you want to preserve.
$endgroup$
– Arthur
Dec 29 '18 at 15:27
add a comment |
$begingroup$
Such bookkeeping concerns also lead to some slightly odd looking definitions, for example the best way to define the degree of the zero polynomial seems to be $-1$.
$endgroup$
– Ian
Dec 29 '18 at 15:09
$begingroup$
@Ian Or $-infty$, depending on which property of degree you want to preserve.
$endgroup$
– Arthur
Dec 29 '18 at 15:27
$begingroup$
Such bookkeeping concerns also lead to some slightly odd looking definitions, for example the best way to define the degree of the zero polynomial seems to be $-1$.
$endgroup$
– Ian
Dec 29 '18 at 15:09
$begingroup$
Such bookkeeping concerns also lead to some slightly odd looking definitions, for example the best way to define the degree of the zero polynomial seems to be $-1$.
$endgroup$
– Ian
Dec 29 '18 at 15:09
$begingroup$
@Ian Or $-infty$, depending on which property of degree you want to preserve.
$endgroup$
– Arthur
Dec 29 '18 at 15:27
$begingroup$
@Ian Or $-infty$, depending on which property of degree you want to preserve.
$endgroup$
– Arthur
Dec 29 '18 at 15:27
add a comment |
3
$begingroup$
Is the empty set a set of integers or a set of polygons?
$endgroup$
– MJD
Dec 29 '18 at 14:52
$begingroup$
Belongs to neither
$endgroup$
– user629353
Dec 29 '18 at 14:54
$begingroup$
So is it to conclude zero polynomial doesn't fit for this classification?
$endgroup$
– user629353
Dec 29 '18 at 14:58
$begingroup$
The symbol 0 is overloaded. Sometimes it refers to the number zero, sometimes it refers to the zero polynomial in $mathbb R[x]$, sometimes it refers to the zero polynomial in $mathbb R[x,y]$, etc. Hopefully the meaning is always clear from context
$endgroup$
– littleO
Dec 29 '18 at 15:01
$begingroup$
So why not its better to regard it not define
$endgroup$
– user629353
Dec 29 '18 at 15:05