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An axiom was a word for an established set of rules or guidelines in logic that one should follow.
In 2371, Lieutenant Joseph Carey was about to eat a Kaylo apple on an unnamed planet in the Delta Quadrant. Neelix warned him not to eat it, warning him that just one bite of it would kill him. Afterward, Neelix told Carey "just remember the old trader's axiom, 'never judge a fruit by its skin.'" (VOY: "State of Flux")
In 2372, Chakotay stated the old axiom "the whole is never greater than the sum of its parts" and suggested that Tuvix, a combination of Tuvok and Neelix from a transporter accident, had disproven it. (VOY: "Tuvix")