Do I write for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
0
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When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3205
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add a comment |
0
$begingroup$
When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3205
$endgroup$
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
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– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
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– Joel Pereira
Dec 8 '18 at 2:03
add a comment |
0
0
0
1
$begingroup$
When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3205
$endgroup$
When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3205
asked Dec 8 '18 at 0:56
mingming
3205
asked Dec 8 '18 at 0:56
mingming
3205
asked Dec 8 '18 at 0:56
mingming
3205
asked Dec 8 '18 at 0:56
mingming
3205
3205
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
add a comment |
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
3
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
add a comment |
0
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3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03