A={ 1, 2, 3, 4 } For group we check associativity, identity and inverse. Clearly set A with composition as operation is associative but i can't figure out the other two things to check whether set of all one-one functions will be a group or not.
2026-04-04 00:50:21.1775263821
Are the set of all one-one functions f: A→A under the composition of mappings, forms a group or not
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Hint (Pigeonhole principle):
An injective function $A\to A$ is surjective if $A$ is finite.