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The 26-year-old YouTuber went the full distance against Mayweather in their exhibition clash at the Hard Rock Stadium in Miami, Florida, on Sunday.
No official winner was crowned from the fight as per the rules, but fans expected that Mayweather would stop Paul in the eight-round bout.
Paul unloaded a flurry of wild shots at the end of the opening round against the unbeaten former five-weight world champ.
Speaking after the fight, the American star claimed that "father time" was catching up with Mayweather.
"He was slower than I thought, father time is catching up with him perhaps," Paul said.
Paul also showed a humble side after the fight as he insisted that it was an "honour" to step in the ring with the boxing legend.
"This is one of the greatest moments of my life... damn, I'm happy," he said.
"You never know with this guy, I'm going to go home thinking, 'Yo, did Floyd let me survive?'
"He's one of the GOATs, and in many ways he controls this sport to the tee, that's what makes him great. It's an honour to grace the ring with him.
"It's an honour to grace the ring with him. Man, this is the coolest thing ever... I'm happy I made it out. He's old, but he's tough to hit."
Paul revealed that he plans to take some time to relax before he makes his next move.
However, the YouTuber teased a second clash with Mayweather as he suggested that he could win in a rematch.
When asked about his future, Paul responded: "I don't know, man, I'm going to go in the water, I'm going to go to the beach.
"Floyd Mayweather-Logan Paul 2? I don't know, let me get a little better... maybe I can end it next time?"
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