Assertion: set | /r/HasProperty | equal
Facets:
value: in v
type: LOCATION
value: in any discrete space
type: LOCATION
value: in l
type: LOCATION
value: by the principle of extensionality
type: OTHER
value: to its interior
type: OTHER
value: to the set
type: OTHER
value: to x
type: OTHER
value: in standard axiomatic set theory
type: OTHER
Source sentences:
text: Two sets are equal if they have precisely the same members.
text: Are these sets equal?
text: In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements; therefore there can be only one set with no elements.
text: does not contain the empty set (that is The union of the sets in P is equal to X (that is ⋃
text: Two sets are equal if and only if they have the same elements.
text: Sets defined by set builder notation are equal if and only if their set builder rules, including the domain specifiers, are equivalent.
text: In particular, both sets are equal to the set { − 1 , 1 } {
text: In any discrete space, since every set is open, every set is equal to its interior.
text: So they are equal (in V and thus in L ).