# What does it mean to demonstrate “por doble inclusión” in Spanish?

What does it mean to demonstrate "por doble inclusión" in Spanish? "By double-counting?" And what is that? thanks

For context, see, e.g., this.

-

I don't know Spanish, but based on similarities with Portuguese I'd say it means "by double inclusion". I infer it's a problem that you need to prove $A = B$ where $A,B$ are sets. Therefore you prove $A \subseteq B$ and $B \subseteq A$.

-
So, "by double inclusion" is a proper mathematical phrase in English? – Geremia Jul 20 '14 at 1:28
@Geremia I believe so. You can always be explicit and say "we prove $A \subseteq B$ and $B \subseteq A$..." – Mark Fantini Jul 20 '14 at 1:35

When you want to prove an equality of two sets, say $X=Y$, you prove $X\subseteq Y$ and $Y\subseteq X$. Thatś what it means.

-
Second equation means probably $Y \subseteq X$. =) – Mark Fantini Jul 20 '14 at 1:26
If you want to be fancy, you can also say «probar por inclusión mutua»... – Mariano Suárez-Alvarez Jul 20 '14 at 1:26
When you say "two sets" you mean "two subsets of a set"... – Qiaochu Yuan Jul 20 '14 at 2:41
@QiaochuYuan, nope. – Mariano Suárez-Alvarez Jul 20 '14 at 2:41
(Two sets are always subsets of a set, their union :-) ) – Mariano Suárez-Alvarez Jul 20 '14 at 2:43