# What is the definition of proper subset?

A set S is a proper subset of a set T if each element of S is also in T and there is at least one element in T that is not in S.
subsets - Definition [suhb-set]
(n.) Set that is a part of a larger set
Source: Dictionary.com
Q&A Related to "What is the definition of proper subset?"
 You could use the axiom of extensionality to make a simpler definition: $$A\subsetneq B =_\mathrm{def} (\forall x\in A. x\in B)\land \lnot(A=B).$$ This is, of course, equivalent to http://math.stackexchange.com/questions/166651/wha...