Am I properly negating the definition of this set?
The statement:
Let $Asubset mathbb{R}$ be defined as follows: $xin A$ if and only if there exists $c>0$ so that
$$ |x-j2^{-k}|geq c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
The negation of the above statement:
$xin A^{c}$ if and only if for all $c>0$, we have that
$$ |x-j2^{-k}|<c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
elementary-set-theory definition
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
asked Dec 1 at 11:33
Joe Man Analysis
33419
add a comment |
The statement:
Let $Asubset mathbb{R}$ be defined as follows: $xin A$ if and only if there exists $c>0$ so that
$$ |x-j2^{-k}|geq c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
The negation of the above statement:
$xin A^{c}$ if and only if for all $c>0$, we have that
$$ |x-j2^{-k}|<c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
elementary-set-theory definition
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
asked Dec 1 at 11:33
Joe Man Analysis
33419
3
'For all' becomes 'there exists' and 'there exists' becomes 'for all'; so you should say for some $jin mathbb Z$ and some integer $k geq 0$.
– Kavi Rama Murthy
Dec 1 at 11:36
add a comment |
The statement:
Let $Asubset mathbb{R}$ be defined as follows: $xin A$ if and only if there exists $c>0$ so that
$$ |x-j2^{-k}|geq c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
The negation of the above statement:
$xin A^{c}$ if and only if for all $c>0$, we have that
$$ |x-j2^{-k}|<c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
elementary-set-theory definition
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
asked Dec 1 at 11:33
Joe Man Analysis
33419
The statement:
Let $Asubset mathbb{R}$ be defined as follows: $xin A$ if and only if there exists $c>0$ so that
$$ |x-j2^{-k}|geq c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
The negation of the above statement:
$xin A^{c}$ if and only if for all $c>0$, we have that
$$ |x-j2^{-k}|<c2^{-k} $$
holds for all $jin mathbb{Z}$ and integers $kgeq 0$.
elementary-set-theory definition
elementary-set-theory definition
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
asked Dec 1 at 11:33
Joe Man Analysis
33419
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
asked Dec 1 at 11:33
Joe Man Analysis
33419
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
edited Dec 1 at 14:11
Andrés E. Caicedo
64.7k8158246
64.7k8158246
asked Dec 1 at 11:33
Joe Man Analysis
33419
asked Dec 1 at 11:33
Joe Man Analysis
33419
asked Dec 1 at 11:33
Joe Man Analysis
33419
33419
3
'For all' becomes 'there exists' and 'there exists' becomes 'for all'; so you should say for some $jin mathbb Z$ and some integer $k geq 0$.
– Kavi Rama Murthy
Dec 1 at 11:36
add a comment |
3
'For all' becomes 'there exists' and 'there exists' becomes 'for all'; so you should say for some $jin mathbb Z$ and some integer $k geq 0$.
– Kavi Rama Murthy
Dec 1 at 11:36
3
3
'For all' becomes 'there exists' and 'there exists' becomes 'for all'; so you should say for some $jin mathbb Z$ and some integer $k geq 0$.
– Kavi Rama Murthy
Dec 1 at 11:36
'For all' becomes 'there exists' and 'there exists' becomes 'for all'; so you should say for some $jin mathbb Z$ and some integer $k geq 0$.
– Kavi Rama Murthy
Dec 1 at 11:36
add a comment |
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3
'For all' becomes 'there exists' and 'there exists' becomes 'for all'; so you should say for some $jin mathbb Z$ and some integer $k geq 0$.
– Kavi Rama Murthy
Dec 1 at 11:36