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The race ended in a tie. The House of Representatives held a special runoff vote. Alexander wrote nasty comments about Aaron mentioning he was "one of the worst men." Jefferson won the presidency and Aaron settled for Vice-president.
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Alexander opposed him again saying he was "despicable."
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Aaron had enough of Alexander's attacks. He demanded an apology, but when none came he challenged Alexander.
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Both men arrived at Weehawken, New Jersey each with a pistol. They stood 30 feet away from each other, raised their pistols, and shot at the same time. Alexander's shot missed, but Aaron's did not.
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Alexander died the day after the duel from his gunshot wound.