Hello, I am having trouble proving the following theorem:

If A(1)....A(n) are finite pairwise disjoint sets then A(1) U A(2)U.....U A(n)= A(1)+....+A(n)

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- Mar 24th 2011, 01:03 PMqwerty10Addition Rule- Extended
Hello, I am having trouble proving the following theorem:

If A(1)....A(n) are finite pairwise disjoint sets then A(1) U A(2)U.....U A(n)= A(1)+....+A(n) - Mar 24th 2011, 01:21 PMPlato
- Mar 24th 2011, 01:34 PMqwerty10
Yes that was my intended way of writing A(1), unable to do it. The theorem reads exactly what I have wrote above....if the sets are finite pairwise disjoint then the union of all the sets is equal to the addition of all the sets

- Mar 24th 2011, 01:44 PMPlato
Are you translating into English?

That makes no sense in mathematics.

There is a theorem about**counting**. The symbol stands for the number of elements is the finite set .

If is a collection of pairwise disjoint finite sets then .

Is that what is meant by the notation? - Mar 24th 2011, 01:49 PMqwerty10
The theorem is to do with counting so that must be the notation

- Mar 24th 2011, 01:56 PMPlato
- Mar 24th 2011, 02:01 PMqwerty10
That is where my problem lies in the induction proof:

I know to begin with the case n=2 so proving the basic counting principle.

Then I assume true for for n and take an n+1 element set and prove its true.

I am just struggling to write out a formal proof - Mar 24th 2011, 02:12 PMPlato
- Mar 24th 2011, 02:24 PMqwerty10
To prove the basic counting principle do we just simply state AuB=A + B - AnB and AnB=empty set so we just get AuB= A + B? I know there should be cardinality signs around the sets

- Mar 24th 2011, 03:36 PMPlato
Is that a statement? Or is it a question?

Why not learn to post in symbols? You can use LaTeX tags

[tex]\|A\|[/tex] gives