Talk:Subsets of Equidecomposable Subsets are Equidecomposable

Throughout, I have been using $\subseteq$ for "is a subset of" and $\subset$ for "is a proper subset of", i.e. $A \subset B \iff A \subseteq B \land A \ne B$.

This is consistent with the notation for $\le$ and $<$, for example, and (for that and possibly other reasons), I believe it's "better" to use $\subset$ as its context above.

As there is generally confusion as to exactly what $\subset$ may mean in a context, it might be better to use $\subseteq$ unless $\subsetneq$ is specifically meant instead.

In this context I don't know which is meant! --Matt Westwood 22:28, 29 January 2009 (UTC)


 * You're absolutely right. Non-proper subset works just fine here.  There's no reason we can't speak of decompositions of all of $\R^n$, and if $A, B$ are equidecomposable, then $S = A$ clearly yields the subset $T = B$ such that $S, T$ are equidecomposable, and the theorem is trivial.  Zelmerszoetrop 00:15, 30 January 2009 (UTC)