Relation on the set of polynomials
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Consider a relation defined on the set of polynomials, such that two polynomials are related if and only if their indefinite integrals are equal. Is this an equivalence relation?
I'm slightly confused with one thing in this question - since every function has infinitely many indefinite integrals, is something going wrong here? In case the answer is no, then I feel its both reflexive and symmetric, but I'm not sure how to prove its transitivity (or lack of it). So please help me with this question, so that I can strengthen my concepts further on relations.
integration polynomials relations
asked Nov 21 at 15:49
Lakshay Kakkar
61
add a comment |
up vote
1
down vote
favorite
Consider a relation defined on the set of polynomials, such that two polynomials are related if and only if their indefinite integrals are equal. Is this an equivalence relation?
I'm slightly confused with one thing in this question - since every function has infinitely many indefinite integrals, is something going wrong here? In case the answer is no, then I feel its both reflexive and symmetric, but I'm not sure how to prove its transitivity (or lack of it). So please help me with this question, so that I can strengthen my concepts further on relations.
integration polynomials relations
asked Nov 21 at 15:49
Lakshay Kakkar
61
I agree that the definition seems vague. If it means that there is a single polynomial $P(x)$ which has derivative equal to each of the two candidate polynomials, then that makes sense...but of course it just means that the two candidate polynomials must be the same.
– lulu
Nov 21 at 15:51
The relation is bogus. Take it as the indefinite integrals differ by a constant.
– William Elliot
Nov 22 at 4:11
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Consider a relation defined on the set of polynomials, such that two polynomials are related if and only if their indefinite integrals are equal. Is this an equivalence relation?
I'm slightly confused with one thing in this question - since every function has infinitely many indefinite integrals, is something going wrong here? In case the answer is no, then I feel its both reflexive and symmetric, but I'm not sure how to prove its transitivity (or lack of it). So please help me with this question, so that I can strengthen my concepts further on relations.
integration polynomials relations
asked Nov 21 at 15:49
Lakshay Kakkar
61
Consider a relation defined on the set of polynomials, such that two polynomials are related if and only if their indefinite integrals are equal. Is this an equivalence relation?
I'm slightly confused with one thing in this question - since every function has infinitely many indefinite integrals, is something going wrong here? In case the answer is no, then I feel its both reflexive and symmetric, but I'm not sure how to prove its transitivity (or lack of it). So please help me with this question, so that I can strengthen my concepts further on relations.
integration polynomials relations
integration polynomials relations
asked Nov 21 at 15:49
Lakshay Kakkar
61
asked Nov 21 at 15:49
Lakshay Kakkar
61
asked Nov 21 at 15:49
Lakshay Kakkar
61
asked Nov 21 at 15:49
Lakshay Kakkar
61
asked Nov 21 at 15:49
Lakshay Kakkar
61
61
I agree that the definition seems vague. If it means that there is a single polynomial $P(x)$ which has derivative equal to each of the two candidate polynomials, then that makes sense...but of course it just means that the two candidate polynomials must be the same.
– lulu
Nov 21 at 15:51
The relation is bogus. Take it as the indefinite integrals differ by a constant.
– William Elliot
Nov 22 at 4:11
add a comment |
I agree that the definition seems vague. If it means that there is a single polynomial $P(x)$ which has derivative equal to each of the two candidate polynomials, then that makes sense...but of course it just means that the two candidate polynomials must be the same.
– lulu
Nov 21 at 15:51
The relation is bogus. Take it as the indefinite integrals differ by a constant.
– William Elliot
Nov 22 at 4:11
I agree that the definition seems vague. If it means that there is a single polynomial $P(x)$ which has derivative equal to each of the two candidate polynomials, then that makes sense...but of course it just means that the two candidate polynomials must be the same.
– lulu
Nov 21 at 15:51
I agree that the definition seems vague. If it means that there is a single polynomial $P(x)$ which has derivative equal to each of the two candidate polynomials, then that makes sense...but of course it just means that the two candidate polynomials must be the same.
– lulu
Nov 21 at 15:51
The relation is bogus. Take it as the indefinite integrals differ by a constant.
– William Elliot
Nov 22 at 4:11
The relation is bogus. Take it as the indefinite integrals differ by a constant.
– William Elliot
Nov 22 at 4:11
add a comment |
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I agree that the definition seems vague. If it means that there is a single polynomial $P(x)$ which has derivative equal to each of the two candidate polynomials, then that makes sense...but of course it just means that the two candidate polynomials must be the same.
– lulu
Nov 21 at 15:51
The relation is bogus. Take it as the indefinite integrals differ by a constant.
– William Elliot
Nov 22 at 4:11