Expressing the truth set of xâ¤0
Clash Royale CLAN TAG#URR8PPP
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Say I have the following predicate which is in the domain of the integers (Z):
$P(x) : x leqslant 0$
Would the truth set be expressed as:
$x inBbb Z : xleqslant 0$
or
$x inBbb Z : x<0 lor x=0$
or
$x inBbb Z : x inBbb Z^- cup 0$
discrete-mathematics predicate-logic
add a comment |Â
up vote
-3
down vote
favorite
Say I have the following predicate which is in the domain of the integers (Z):
$P(x) : x leqslant 0$
Would the truth set be expressed as:
$x inBbb Z : xleqslant 0$
or
$x inBbb Z : x<0 lor x=0$
or
$x inBbb Z : x inBbb Z^- cup 0$
discrete-mathematics predicate-logic
Which one would you suspect is correct? And why?
â esotechnica
Aug 19 at 8:26
add a comment |Â
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Say I have the following predicate which is in the domain of the integers (Z):
$P(x) : x leqslant 0$
Would the truth set be expressed as:
$x inBbb Z : xleqslant 0$
or
$x inBbb Z : x<0 lor x=0$
or
$x inBbb Z : x inBbb Z^- cup 0$
discrete-mathematics predicate-logic
Say I have the following predicate which is in the domain of the integers (Z):
$P(x) : x leqslant 0$
Would the truth set be expressed as:
$x inBbb Z : xleqslant 0$
or
$x inBbb Z : x<0 lor x=0$
or
$x inBbb Z : x inBbb Z^- cup 0$
discrete-mathematics predicate-logic
edited Aug 19 at 8:24
Graham Kemp
80.5k43275
80.5k43275
asked Aug 19 at 8:20
R. Lee
1
1
Which one would you suspect is correct? And why?
â esotechnica
Aug 19 at 8:26
add a comment |Â
Which one would you suspect is correct? And why?
â esotechnica
Aug 19 at 8:26
Which one would you suspect is correct? And why?
â esotechnica
Aug 19 at 8:26
Which one would you suspect is correct? And why?
â esotechnica
Aug 19 at 8:26
add a comment |Â
2 Answers
2
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Yes. Â Those sets are equivalent and represent the set of integers which satisfy the given predicate.
Indeed, they can be simply represented as: $~~Bbb Z^-cup0$
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Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:
- $xinmathbb Zmid P(x)$
- $x inBbb Z : xleqslant 0$
- $x inBbb Z : x<0 lor x=0$
- $x inBbb Z : x inBbb Z^- cup 0$
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Yes. Â Those sets are equivalent and represent the set of integers which satisfy the given predicate.
Indeed, they can be simply represented as: $~~Bbb Z^-cup0$
add a comment |Â
up vote
0
down vote
Yes. Â Those sets are equivalent and represent the set of integers which satisfy the given predicate.
Indeed, they can be simply represented as: $~~Bbb Z^-cup0$
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Yes. Â Those sets are equivalent and represent the set of integers which satisfy the given predicate.
Indeed, they can be simply represented as: $~~Bbb Z^-cup0$
Yes. Â Those sets are equivalent and represent the set of integers which satisfy the given predicate.
Indeed, they can be simply represented as: $~~Bbb Z^-cup0$
answered Aug 19 at 8:28
Graham Kemp
80.5k43275
80.5k43275
add a comment |Â
add a comment |Â
up vote
0
down vote
Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:
- $xinmathbb Zmid P(x)$
- $x inBbb Z : xleqslant 0$
- $x inBbb Z : x<0 lor x=0$
- $x inBbb Z : x inBbb Z^- cup 0$
add a comment |Â
up vote
0
down vote
Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:
- $xinmathbb Zmid P(x)$
- $x inBbb Z : xleqslant 0$
- $x inBbb Z : x<0 lor x=0$
- $x inBbb Z : x inBbb Z^- cup 0$
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:
- $xinmathbb Zmid P(x)$
- $x inBbb Z : xleqslant 0$
- $x inBbb Z : x<0 lor x=0$
- $x inBbb Z : x inBbb Z^- cup 0$
Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:
- $xinmathbb Zmid P(x)$
- $x inBbb Z : xleqslant 0$
- $x inBbb Z : x<0 lor x=0$
- $x inBbb Z : x inBbb Z^- cup 0$
answered Aug 19 at 8:50
drhab
87.7k541119
87.7k541119
add a comment |Â
add a comment |Â
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Which one would you suspect is correct? And why?
â esotechnica
Aug 19 at 8:26