Asymptote

The thing about an asymptote is that the curve gets nearer and nearer to the line and never, not once in all of forever, touches it. June had drawn a hundred of them on a hundred whiteboards. She understood them the way she understood her own pulse, which is to say completely and without comfort.

"You're doing the thing," Sam said, "where you stare at the board and forget I'm holding two coffees."

She took the nearer cup. Their fingers did the small arithmetic of not-quite-touching, that old function, that curve she knew by heart.

"I was thinking about limits," she said.

"You're always thinking about limits."

"As x approaches infinity," she said, and stopped, because the rest of the sentence was a cliff.

Sam set his coffee down. He had a way of giving a problem his whole attention that had undone her in their first week as office-mates and undid her now. "June," he said. "Some functions are discontinuous. You can just — jump. You can be at the value. You don't have to approach it forever."

"That's not rigorous."

"Marry the rigor later." He smiled. "Right now I'm asking you to be a step function."

She thought about the proof she had been writing in the margins of every day for a year. She thought about how the limit existed even when the value was undefined, how the whole edifice of calculus was built on the audacity of saying *and here is where it would arrive, if it could.*

She closed the distance. The curve met the line. Somewhere a textbook was wrong, and she did not care.