I see no paradox at all. I was delighted when I was back in high school (a very very long time ago ... maybe an infinite time ago), and a completely valid argument under the generally accepted theories of maths at the time. It's a fantastical journey into Cantor and his amazing "rules" for talking about infinity. But that's strictly a mathematical idea, and at that level you can't easily defy it, but you're welcome to offer another theory of your own. (;-{}

And the question of whether the continuum = aleph1? Which is a beautiful question to ponder while on sabbattical. Ah, the fresh air!

It's a mathematical thing more than a physical thing. We don't really ABSOLUTELY know if any sort of infinity exists outside our brains. GregR