👉 In mathematics, an "otiose" or "otio", or "otiose", set is a subset of a set that contains no elements that are "identical to themselves". In other words, it's a set where every element is either in one of two sets (the first being the subset and the second being its complement) or not in any set at all. This property can be used to simplify mathematical proofs by avoiding the use of notation for such sets.