Can a set that is closed under a binary operation have inverses for all of its elements.. without the existence of an identity element?
127664
Inverse elements in the absence of identities/associativity.
64658
How many associative binary operations for a set of two elements?
84609
Unary intersection of the empty set
126025
Computing the inverse of a permutation
67208
Can we say that there exist an integer $n$ such $A+nB$ invertible?
37951
proof detail concerning bijection between a set and its power set
148992
A finite set is closed
97951
Is the void set (∅) a proper subset of every set?
21114
$S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
28539
Does any uncountable set contain two disjoint uncountable sets?
114830
bit-wise operation unary ~ (invert)
18308
Coset multiplication giving a well defined binary operation
89506
Union of disjoint sets : Equivalence relations
65549
What is the cartesian product of an empty set of sets?
144181
Given an arbitrary set $X$, can one always find an element outside $X$?
26008
Why there is a unique empty set?
146231
Let X be a set with an associative binary operation ◦ with identity e. Suppose every element of X satisﬁes x ◦ x = e. Prove that ◦ is commutative.