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In Mathematics, ‘trivial’ has both a social meaning and a technical meaning. The social meaning is ‘easy’, and the technical meaning is ‘not reducible’. For example, the Pythagorean triple 3-4-5 might be considered trivial in the sense of ‘easy’, but it is nontrivial in the sense that it is not reducible to a set of smaller positive integers, unlike, say, the Pythagorean triple 6-8-10, whose status as a Pythagorean triple can be ascribed to the fact that multiplying the members of a Pythagorean triple by the same number results in another Pythagorean triple. Therefore, given that 3-4-5 is a Pythagorean triple, it automatically follows that (2×3)-(2×4)-(2×5), in other words, 6-8-10, is a Pythagorean triple.
keywords: Mathematics, phraseology