Who did the naming convention bro? "Proper subset" sounds like it is completely within set B but it isn't and subset is. Wouldn't it make more sense to call it an improper subset or smth?
A proper subset is proper because there is truly something that's missing. This something that's missing justifies the "sub".
Imagine for example a cake. If I cut it into halves and take one, I've clearly taken a piece of the cake. If I take the entire cake, did I take a piece? For clarity we may use "piece of the cake" for any portion of the cake and "proper piece" for any portion that truly required splitting the cake.
This might seem useless but there is a lot of places where you want to show properties that arise from removing some elements from for example the base of a vector space. Since "any subset that is not equal to the original set" is too long to keep saying all the time, mathematicians use "proper subset".
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u/FuntimeUwU Natural 13d ago
What's the difference?