Outside the New York Public Library, a middle-aged man with a heavy Brooklyn accent walked up to him, hand outstretched.

"Mayor Bloomberg, you did a great job," the man said. "Thank you for being our mayor for the past 12 years."

The mayor broke his stride, turned and smiled.

"I wish you could stay on," the man added.

The mayor's smile widened.

So it went on Tuesday, as the mayor who lives by numbers kept a watchful eye on the clock. At an interfaith breakfast inside the library, he flipped open his black leather iPad and started to read from a speech with a stark heading at the top. "LAST DAY," it read.

One by one, religious leaders took to the microphone, offering him praise from a source that seemed to humble even the billionaire mayor: God.

"This great city of New York has never flourished more than today," declared a rabbi from Staten Island. "We have been blessed by Mayor Michael Bloomberg's presence among us."

"The psalmist declares, 'One who does these things shall never falter,'" the rabbi added.

A sheikh from the Bronx was effusive, praising Allah, then Mr. Bloomberg: "We are here to pray for you. Because under your leadership, Mr. Mayor, the city is safer, cleaner, nicer, healthier and friendlier."

"Mr. Mayor, under your leadership, you did not fail any community in the city."

When it was his turn to talk, Mr. Bloomberg abandoned his usual recitation of legacy-burnishing statistics. Instead, he simply thanked those in the room, reminding them that they, not he, were the on-the-ground soothers and problem-solvers who had made the city work.

"I have always been envious of you," he said. "Because you work at the real level where the real problems are."

"At my level, you talk about them, you look at the grand scheme, you look at averages," Mr. Bloomberg continued. "You have to deal with big numbers. Big numbers are easy to deal with. It's much tougher when you deal one on one, looking at a person right in the eye who has a problem."

It was his final speech as mayor.

A choir of children began to sing "When You Believe," a 1998 ballad made famous by Whitney Houston and Mariah Carey.

Mr. Bloomberg looked on, tapping his foot lightly, but seemed distracted. His head drifted to the crowd, which he took in with a long wistful sweep, his eyes growing glassy.