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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.

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2 Answers 2

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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 $B \subseteq A$.

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So, "by double inclusion" is a proper mathematical phrase in English? –  Geremia Jul 20 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 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.

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Second equation means probably $Y \subseteq X$. =) –  Mark Fantini Jul 20 at 1:26
4  
If you want to be fancy, you can also say «probar por inclusión mutua»... –  Mariano Suárez-Alvarez Jul 20 at 1:26
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When you say "two sets" you mean "two subsets of a set"... –  Qiaochu Yuan Jul 20 at 2:41
    
@QiaochuYuan, nope. –  Mariano Suárez-Alvarez Jul 20 at 2:41
    
(Two sets are always subsets of a set, their union :-) ) –  Mariano Suárez-Alvarez Jul 20 at 2:43

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