Give an example, if possible, of a denumerable collection of finite sets whose union is finite.

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- Nov 14th 2010, 11:52 AMveronicak5678Denumerability
Give an example, if possible, of a denumerable collection of finite sets whose union is finite.

- Nov 14th 2010, 12:00 PMFernandoRevilla
- Nov 14th 2010, 12:03 PMveronicak5678
Thanks for answering, but I don't understand the set. What is {a}?

- Nov 14th 2010, 12:06 PMFernandoRevilla
- Nov 14th 2010, 12:07 PMJhevon
haha, it's a letter, well, a set containing a letter. doesn't matter what a is. all your sets have one element, and that is called a. you have a denumerable collection of 1-element sets (hence finite sets), whose union is a 1-element set (hence finite). if it bothers you so much, you can replaced a with whatever you want. like a number or something.

- Nov 14th 2010, 12:11 PMveronicak5678
Oh! I see. I didn't understand where the n came into it. Thanks.

- Nov 14th 2010, 01:39 PMMoeBlee
- Nov 14th 2010, 02:42 PMFernandoRevilla
- Nov 14th 2010, 03:01 PMJhevon
the sets were not required to be denumerable, the collection, or "number", of sets are to be. each set should be finite. i agree with

**FernandoRevilla**'s interpretation (he wasn't very rigorous in his definition to begin with, but i think he got the idea across). And i don't think it would work without making a lot of the sets (a countably infinite amount of them) the same set. - Nov 14th 2010, 03:05 PMPlato
- Nov 14th 2010, 03:14 PMJhevon
- Nov 14th 2010, 05:52 PMtopspin1617
Maybe they are distinguishing between a "collection of sets" and a "set of sets" to allow something like the solution given here.... maybe a "collection" means a multiset? =P

Ah, ambiguities :) - Nov 14th 2010, 06:22 PMDrexel28
- Nov 15th 2010, 10:24 AMMoeBlee
If you tell me "X is a denumerable collection of finite sets whose union is finite" then I take that as:

X is denumerable

Every member of X is finite

The union of X is finite

The word "collection" has no special meaning here other than 'set' unless otherwise specified.

In particular, it's a jump to regard "collection" as an indexing function unless that is specified.