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## Main Question or Discussion Point

I am not a mathematician, I am a physicist. Out of curiosity, how big is the following set?

Let me first define:

A_0 = a point

A_1 = the reals

A_2 = the reals^2 (the plane)

A_3 = the reals^3

.

.

.

The set I want to know the size of is the sum (union) of all the A_n sets, where n goes to infinity. Also, can i assign a cardinality?

Let me first define:

A_0 = a point

A_1 = the reals

A_2 = the reals^2 (the plane)

A_3 = the reals^3

.

.

.

The set I want to know the size of is the sum (union) of all the A_n sets, where n goes to infinity. Also, can i assign a cardinality?