On: Cantor visits Hilbert's Hotel

I'll put up some references here to Hilbert's Hotel

http://www.bbc.co.uk/dna/h2g2/A4080467

http://www.bbc.co.uk/dna/h2g2/A593552

http://faculty.cua.edu/glenn/187f09/hilbert_hotel.pdf

to help people follow your argument. I see you are getting into the power set when you write, "There are many, many sub-committees that have to convene. In fact, every possible sub-committee."