How many points are there in the following set? [on hold]
up vote
0
down vote
favorite
Let us consider the following set:
$A={(x, y, z) in Bbb{R}timesBbb{R}timesBbb{R} : ax+by+c=0,z=0 },cneq 0$ and
$B={(x, y, z) in Bbb{R}timesBbb{R} timesBbb{R} : ax+by=0,z=0}$.
Then $A, B$ are two infinite sets. How to determine the cardinality of the set $A-B$?
cardinals 3d plane-geometry
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
put on hold as off-topic by user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did 2 days ago
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
Let us consider the following set:
$A={(x, y, z) in Bbb{R}timesBbb{R}timesBbb{R} : ax+by+c=0,z=0 },cneq 0$ and
$B={(x, y, z) in Bbb{R}timesBbb{R} timesBbb{R} : ax+by=0,z=0}$.
Then $A, B$ are two infinite sets. How to determine the cardinality of the set $A-B$?
cardinals 3d plane-geometry
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
put on hold as off-topic by user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did 2 days ago
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let us consider the following set:
$A={(x, y, z) in Bbb{R}timesBbb{R}timesBbb{R} : ax+by+c=0,z=0 },cneq 0$ and
$B={(x, y, z) in Bbb{R}timesBbb{R} timesBbb{R} : ax+by=0,z=0}$.
Then $A, B$ are two infinite sets. How to determine the cardinality of the set $A-B$?
cardinals 3d plane-geometry
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
Let us consider the following set:
$A={(x, y, z) in Bbb{R}timesBbb{R}timesBbb{R} : ax+by+c=0,z=0 },cneq 0$ and
$B={(x, y, z) in Bbb{R}timesBbb{R} timesBbb{R} : ax+by=0,z=0}$.
Then $A, B$ are two infinite sets. How to determine the cardinality of the set $A-B$?
cardinals 3d plane-geometry
cardinals 3d plane-geometry
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
edited Dec 1 at 4:21
Andrés E. Caicedo
64.4k8157245
64.4k8157245
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
asked Dec 1 at 3:49
Md Kutubuddin Sardar
133
133
put on hold as off-topic by user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did 2 days ago
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did 2 days ago
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
I am assuming $a$, $b$, and $c$ are fixed real numbers.
If $(x,y,z)in B$, then $z=0$ and $ax+by=0$. But then $ax+byneq -c$, since $cneq 0$, so $(x,y,z)notin A$. Therefore, $A-B=A$.
This is really just a proof that two parallel (but distinct) lines have no points of intersection!
answered Dec 1 at 5:03
Lucas
666
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
I am assuming $a$, $b$, and $c$ are fixed real numbers.
If $(x,y,z)in B$, then $z=0$ and $ax+by=0$. But then $ax+byneq -c$, since $cneq 0$, so $(x,y,z)notin A$. Therefore, $A-B=A$.
This is really just a proof that two parallel (but distinct) lines have no points of intersection!
answered Dec 1 at 5:03
Lucas
666
add a comment |
up vote
1
down vote
I am assuming $a$, $b$, and $c$ are fixed real numbers.
If $(x,y,z)in B$, then $z=0$ and $ax+by=0$. But then $ax+byneq -c$, since $cneq 0$, so $(x,y,z)notin A$. Therefore, $A-B=A$.
This is really just a proof that two parallel (but distinct) lines have no points of intersection!
answered Dec 1 at 5:03
Lucas
666
add a comment |
up vote
1
down vote
up vote
1
down vote
I am assuming $a$, $b$, and $c$ are fixed real numbers.
If $(x,y,z)in B$, then $z=0$ and $ax+by=0$. But then $ax+byneq -c$, since $cneq 0$, so $(x,y,z)notin A$. Therefore, $A-B=A$.
This is really just a proof that two parallel (but distinct) lines have no points of intersection!
answered Dec 1 at 5:03
Lucas
666
I am assuming $a$, $b$, and $c$ are fixed real numbers.
If $(x,y,z)in B$, then $z=0$ and $ax+by=0$. But then $ax+byneq -c$, since $cneq 0$, so $(x,y,z)notin A$. Therefore, $A-B=A$.
This is really just a proof that two parallel (but distinct) lines have no points of intersection!
answered Dec 1 at 5:03
Lucas
666
edited Dec 1 at 5:19
answered Dec 1 at 5:03
Lucas
666
answered Dec 1 at 5:03
Lucas
666
answered Dec 1 at 5:03
Lucas
666
666
add a comment |
add a comment |
