ARREN, Ohio - Al Gore and George W. Bush each claimed victory yesterday in their first debate, with thousands of supporters cheering in agreement during a pair of battleground-state rallies that marked a full flowering of the presidential campaign.
Under a brilliant fall sunshine, in a city square teeming with about 5,000 people, and after an introduction by a recent Olympic gold medalist, the vice president laid out his view of the decision facing voters a little more than a month away.
''This choice is a choice between going in the right direction, towards a stronger economy with more jobs and higher incomes, or a U-turn back to the old ways where they concentrate on those at the very top,'' the Democratic nominee said.
Across the border in Pennsylvania, Bush addressed an equally enthusiastic audience at West Chester University in suburban Philadelphia. The Republican candidate, too, described the election as a clear choice: between his faith in the people and Gore's belief in big government.
Bush said that distinction was evident during the candidates' debate Tuesday at the University of Massachusetts at Boston.
''I enjoyed that debate because it gave Americans from all walks of life a chance to see us directly,'' the governor of Texas said. ''America got to see a difference in philosophy.''
Thousands of students greeted him with the refrain of his signature line from the debate: ''No fuzzy math! No fuzzy math!'' they cried.
In his own reference to the debate, Gore took offense at Bush questioning his character over fund-raising problems during the 1996 campaign.
''I don't know about you,'' Gore said, ''but I think even though Governor Bush and I have a lot of differences, personally, I think it's better to spend time attacking American problems than attacking people personally. ... I think we should build our country up instead of tearing somebody else down.''
He was cheered by his heavily union audience in this blue-collar community. Joining the vice president and his wife, Tipper, on stage was Diana Munz, an Ohio swimmer who won a gold and a silver medal at the summer Olympics in Australia.
Before leaving Massachusetts for Pennsylvania, Bush accepted the endorsement of the Massachusetts State Police union, which has 1,900 members. At an appearance at the Logan Airport Hilton - presumably his last Boston appearance of the campaign - Bush also accepted a T-shirt with the Massachusetts State Police logo and a Bush-Cheney inscription on back.
''Governor Cellucci tells me we've got an outside shot here in Massachusetts,'' Bush said. ''If that's the case, even an outside shot makes me encouraged.''
Behind the lofty stump speeches, aides to both candidates attacked the credibility of comments each candidate made during their 90-minute debate. The second of their three face-offs is Wednesday in Winston-Salem, N.C.
The Gore campaign's biggest criticism centered on Bush's casual statement that he would use the federal budget surplus to help defray the estimated $1 trillion cost of implementing his Social Security plan. Under that proposal, workers would invest some of their Social Security payroll tax in the stock market.
Previously, the governor has said that he would use about half of the $4.56 trillion surplus to maintain the flow of payroll taxes into Social Security. He alloted another quarter for emergencies and new spending proposals, and the remaining quarter for a tax cut.
''Even using George W. Bush's imaginary numbers, the math does not add up, and what it translates into is a very irresponsible plan that will undermine our economy,'' said Gore's spokesman, Chris Lehane.
Meanwhile, in private interviews, Gore aides conceded that the vice president sounded bad when he sighed several times during the debate. They said he told them he did not realize his microphone was live, that he thought it was turned off when the TV camera was pointed away.
''There will be a silencing of the sighs,'' one top adviser said.
Despite some early focus-group numbers suggesting Gore had won on technical points, the atmosphere in the Bush campaign was upbeat, and some aides suggested he would be more at ease next time around.
Johnson, traveling with Gore, reported from Ohio; Kornblut, traveling with Bush, reported from Pennsylvania.
