Sep 1, 2015 · The other subset of $A$, $\ {1,2\}$, is not a proper subset of $A$, since it equals $A$. So basically, for any non-empty set $A$, if you think of all of its subsets, then all but one of them is proper.

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 …

A set A is a proper subset of a set B if A is a subset of B and there is at least one element of B that's not an element of A. Thus, the void set is a subset of all sets, and it's a proper subset of every set except …

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 …

Oct 3, 2018 · 50 If the book distinguishes between $\subset$ and $\subseteq$, then most likely the former symbol denotes proper inclusion, so $\ {0\}\subset\ {0\}$ is false. The latter symbol instead will …

Following what I had worked out above, what I am wondering is - Why differentiate between subset and proper subset? Given the fact that equality if provided by Definition 2, it seems to me that the …

Nov 15, 2018 · Prove B is a proper subset of A Ask Question Asked 7 years, 1 month ago Modified 4 years, 8 months ago

Jan 22, 2015 · The use of $\subset$ for proper subset and $\subseteq$ for subset is obviously motivated by analogy with $<$ and $\le$. On the other hand, using $\subsetneq$ for proper subset and …

Oct 25, 2020 · I like using $\subset$ for subset or equal. I find that I rarely need to talk about proper subsets. You can use whatever you want as long as you make it clear to the reader what you mean.

Oct 12, 2015 · I think the "modern way," as implied by the partial-order nature of subsets, would be to use $\subseteq$ for any subset and $\subset$ for proper subset, paralleling to $\leq$ and $<$. But I …