Mixing
Interior of a subset of $mathbb{R}^3$ where $(x,y)inmathbb{Q}^2$
$begingroup$
I'm having problems to visualize the interior and accumulation points of this set $$
D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
$$
I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?
general-topology multivariable-calculus
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
$endgroup$
add a comment |
$begingroup$
I'm having problems to visualize the interior and accumulation points of this set $$
D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
$$
I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?
general-topology multivariable-calculus
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
$endgroup$
add a comment |
$begingroup$
I'm having problems to visualize the interior and accumulation points of this set $$
D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
$$
I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?
general-topology multivariable-calculus
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
$endgroup$
I'm having problems to visualize the interior and accumulation points of this set $$
D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
$$
I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?
general-topology multivariable-calculus
general-topology multivariable-calculus
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
asked Jan 18 at 8:54
Raúl AsteteRaúl Astete
516
516
add a comment |
add a comment |
1 Answer
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$begingroup$
The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
$endgroup$
add a comment |
$begingroup$
The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
$endgroup$
add a comment |
$begingroup$
The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
$endgroup$
The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
answered Jan 18 at 8:56
José Carlos SantosJosé Carlos Santos
164k22131234
164k22131234
add a comment |
add a comment |
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