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I wish to show that an algebra is closed under finite unions.

Can I do it using induction on the number of unions performed over the elements of my algebra say $\mathcal{A}$ instead of induction on the number of elements in $\mathcal{A}$ involved in the union such as the one used in

understanding closed under finite intersection notation

and in

Is strong induction necessary in proving that an algebra is closed under finite union? ?

Is it more appropriate to do induction in the number of unions, instead on the number of elements?

Jr Antalan
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  • What kind of algebra are you talking about? And what sets are you taking he Union of? – TomGrubb Oct 04 '18 at 14:03
  • @TomGrubb I am talking about algebra $\mathcal{A}$ that is a collection of subsets of a set $X$ that satisfies the following properties: (i) If $A\in\mathcal{A}$ so is $A'$ and (ii) If $A$ and $B$ are in $\mathcal{A}$ so is $A\cup B$. – Jr Antalan Oct 04 '18 at 14:06
  • Yes, you should use induction over the number of elements in the union. Don't forget to deal with the special case of the empty union. – Mees de Vries Oct 04 '18 at 14:25
  • @MeesdeVries do you mean that I cant use induction over union? Thanks in advance – Jr Antalan Oct 04 '18 at 14:28
  • What...? I said you should to induction over the number of elements that appear in the union. – Mees de Vries Oct 04 '18 at 14:29
  • @MeesdeVries is it better than the induction over the number of unions performed? Why? Sorry for my follow up questions. – Jr Antalan Oct 04 '18 at 14:34

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