Web Reference: Sep 1, 2015 · Subset is more general than proper subset (like green is more general than dark green -- everything that is dark green is green, but not everything that is green is dark green). Jul 25, 2017 · So A can equal B. There's only one A for a given B such that A is a subset of B, but not a proper subset of B. "Improper subset" is a funny, uncommon way of describing two sets that are equal. The even numbers are an "improper subset" of the multiples of two. Silly. Not a practical way to speak about sets in most situations. Sep 10, 2023 · But "proper" can also mean : "a subset different from the set itself" (which is an obvious subset) , allowing also the empty set. Personally , I would prefer the first definition in analogy to a factor of a number , where we usually also mean a nontrivial factor ($1$ and the number itself are excluded).
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