Scott, the best way to think of sharps is via mice. Think of x^#$x^\#$ as a mouse over x$x$ with one measure which is iterable. R^#$\mathbb R^\#$ is a mouse over R$\mathbb R$ with one measure which is iterable. Things become very easy ones you make the move from sharps as reals or sets of reals or etc to sharps as mice.
Seeing how this question was bumped anyway, might as well LaTeX this answer up.
Asaf Karagila
- 39.8k
- 8
- 135
- 283