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disjoint
Mathworld explains the Axiom of Choice as follows:<ref name="mathworld">http://mathworld.wolfram.com/AxiomofChoice.html</ref>
Mathworld explains the Axiom of Choice as follows:<ref name="mathworld">http://mathworld.wolfram.com/AxiomofChoice.html</ref>
::Given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets.
::Given any set of mutually [[disjoint]] nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets.
Therefore, "We can choose one [[element]] from every element of a nonempty set of disjoint sets and this process by which we choose these sets will set up a new set."
Therefore, "We can choose one [[element]] from every element of a nonempty set of disjoint sets and this process by which we choose these sets will set up a new set."