vacuous
Suppose is a set and is a property defined as follows:
has property if and only if | ||
satisfies condition satisfies condition |
where condition and condition define the property. If condition is never satisfied then satisfies property vacuously.
Examples
-
1.
If is the set and is the property defined as above with condition is a infinite subset of , and condition contains . Then has property vacously; every infinite subset of contains the number [1].
-
2.
The empty set is a Hausdorff space (vacuously).
-
3.
Suppose property is defined by the statement :
The present King of France does not exist.
Then either of the following propositions is satisfied vacuously.
The present king of France is bald.
The present King of France is not bald.
References
- 1 Wikipedia http://en.wikipedia.org/wiki/Vacuous_truthentry on Vacuous truth.
Title | vacuous |
---|---|
Canonical name | Vacuous |
Date of creation | 2013-03-22 14:42:27 |
Last modified on | 2013-03-22 14:42:27 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 9 |
Author | matte (1858) |
Entry type | Definition |
Classification | msc 00A20 |
Synonym | vacuously |
Synonym | vacuously true |
Synonym | vacuous truth |