How many points are there in the following set? [closed]
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
64.7k8158246
asked Dec 1 at 3:49
MKS
133
closed as off-topic by Saad, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did Dec 1 at 17:10
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." – Saad, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
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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
64.7k8158246
asked Dec 1 at 3:49
MKS
133
closed as off-topic by Saad, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did Dec 1 at 17:10
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." – Saad, 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 |
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
64.7k8158246
asked Dec 1 at 3:49
MKS
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
64.7k8158246
asked Dec 1 at 3:49
MKS
133
edited Dec 1 at 4:21
Andrés E. Caicedo
64.7k8158246
asked Dec 1 at 3:49
MKS
133
edited Dec 1 at 4:21
Andrés E. Caicedo
64.7k8158246
edited Dec 1 at 4:21
Andrés E. Caicedo
64.7k8158246
edited Dec 1 at 4:21
Andrés E. Caicedo
64.7k8158246
64.7k8158246
asked Dec 1 at 3:49
MKS
133
asked Dec 1 at 3:49
MKS
133
asked Dec 1 at 3:49
MKS
133
133
closed as off-topic by Saad, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did Dec 1 at 17:10
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." – Saad, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Saad, spaceisdarkgreen, Brahadeesh, Vidyanshu Mishra, Did Dec 1 at 17:10
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." – Saad, 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
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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
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 |
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 |
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 |
