the free boolean algebra with κ generators, where κ is a finite or infinite cardinal number, may be realized as the collection of all clopen subsets of {0,1}, given the product topology assuming that {0,1} has the discrete topology. for each α<κ, the α"th" generator is the set of all elements of {0,1} whose α"th" coordinate is 1. in particular, the free boolean algebra with formula_5 generators is the collection of all clopen subsets of a cantor space, sometimes called the cantor algebra. surprisingly, this collection is countable. in fact, while the free boolean algebra with "n" generators, "n" finite, has cardinality formula_1, the free boolean algebra with formula_5 generators, as for any free algebra with formula_5 generators and countably many finitary operations, has cardinality formula_5.