# Is a set the union of its finite subsets?

• Oct 13th 2009, 10:57 AM
ENRIQUESTEFANINI
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.
• Oct 13th 2009, 11:21 AM
minkyboodle
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.
• Oct 13th 2009, 11:26 AM
Plato
Quote:

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.
$\displaystyle \bigcup\limits_{n \in A} {\{ n\} } = ?$

$$A~,~\mathcal{A}~,~\mathbb{A}$$ gives $\displaystyle A~,~\mathcal{A}~,~\mathbb{A}$
• Oct 13th 2009, 01:09 PM
ENRIQUESTEFANINI
It was very kind of you. A short time after writing I saw the key was considering the singletons. Best regards,

Enrique.