"ℵ₀ < ℵ₁"

She wrote it on the whiteboard the way people write suicide notes--small, careful, final. Dr. Marsh had spent eleven years looking into infinity. Now infinity had decided to look back.

It started with the counting. She would count the tiles on her office ceiling--thirty-six, always thirty-six--but then, some nights, she'd count them again and get thirty-seven. Not a new tile. The same thirty-six tiles, only occupying more positions than there were positions to occupy. She stopped sleeping in the office after the night she counted to forty-one and recognized none of the numbers as ones she'd said before.

A hundred years ago, Cantor went mad proving this (or so she would tell her graduate students, half-joking): There's more than one infinity. There's the smallest infinity, which is just the counting numbers like one, two, three, and so on, forever. And then there's a bigger infinity, the infinity of all possible decimals, all possible points on a line, uncountably many, too many to ever list. Because if you try, you'll create new numbers, ones that aren't on any list. That's what Georg Cantor proved in 1891.

Dr. Marsh remembered the student who had definitely sat in the front row. Nobody else--not his classmates, not the admissions office, not her computer records--remembered him ever enrolling. That was strange. She remembered the proof she'd definitely written, the one that was now gone from six notebooks at once, the pages again smooth and virgin where the ink should have been. That was strange, too. Things that should have existed exactly once were existing zero times, or twice, or ℵ₀ times, and she began to suspect something stranger yet--that she, herself, had become a new number, one not on any list.