# Thread: Is a set the union of its finite subsets?

1. ## Is a set the union of its finite subsets?

Hi:
Let A be a set. Is A the union of all its finite subsets? By the way: how can I write a capital cursive in Latex? Regards and thanks for reading.

Enrique.

2. I would say yes it is. A union is everything included in the selected sets. Here, there is only one set, and we are not excluding any part of it, so it is in Union of itself. I am no expert., just trying to help.

3. Originally Posted by ENRIQUESTEFANINI
Hi:
Let A be a set. Is A the union of all its finite subsets? By the way: how can I write a capital cursive in Latex? Regards and thanks for reading.
Consider this very carefully.
$\bigcup\limits_{n \in A} {\{ n\} } = ?$

$$A~,~\mathcal{A}~,~\mathbb{A}$$ gives $A~,~\mathcal{A}~,~\mathbb{A}$

4. It was very kind of you. A short time after writing I saw the key was considering the singletons. Best regards,

Enrique.