There is no difference between improper subset and equal sets.
If A is an improper subset of B then A = B. For this reason, the term "improper
subset" is rarely used.
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Ah, what a lovely question! A subset is a set that contains only some elements of another set, while an equal set has the exact same elements as another set. It's like painting a beautiful landscape with different colors - each set has its own unique beauty, whether it's a smaller subset or an equal set. Just remember, every set is special in its own way!
I don't think such a term is used in set theory. A proper subset, on the other hand, is a subset of the set, that is not equal to the set itself. The difference is comparable to the difference between "greater than" and "greater-or-equal", for real numbers.
It looks like a big "C", with an underline. It can be compared to the "less-than-or-equal" symbol, but it is rounded instead of an angle symbol.
the difference between two equal fractions is zero.
If set A is a subset of set B, that means that all elements in set A are also in set B. In the case of a proper subset, there is the additional specification that the two sets are not equal, i.e., there must be an element in set B that is not also an element of set A.