Still, in the years since Mr. Bloomberg left office, polls have shown a wide-scale distrust of billionaires, once celebrated as the pinnacle of American achievement. Many Democratic candidates have done the math — 99.999999 percent is larger than .000001 percent — and campaigned accordingly.

Senator Bernie Sanders has said he does not believe billionaires should exist at all. Ms. Warren has delighted in taunting them with a customized tax-bill calculator on her website, infusing her stump speech with a faux-sympathetic “awwwwww” after telling voters about the very-upper-class opposition to her wealth tax proposal.

At an event in Greensboro, N.C., on Thursday, which found Ms. Warren onstage for a word association game with an interviewer, one of the prompts was “billionaires.”

“Boohoo,” she said, breaking into mock tears.

Such is the unsubtlety of the nation’s present debate: a real-time collision of topple-the-plutocracy candidates and actual plutocrats in the same presidential field, injecting the race with a raft of questions that suddenly seem less academic:

In a primary consumed by talk of corporate excesses, with top candidates mostly in their 70s, can Mr. Bloomberg, a 77-year-old titan of high finance, really find a major audience?

Might his entry only boost the progressive candidates whose ascent — coupled with the stumbles of former Vice President Joseph R. Biden Jr. — so troubled Mr. Bloomberg in the first place, supplying them with another flesh-and-blood billionaire against whom they can make their case?