Floyd Mayweather Jr. -- You Look Like Someone I Know! Hangs with Ruby Rose (PHOTO)

Floyd Mayweather Jr. taught Hollywood "It" girl Ruby Rose a few things about boxing -- during a Las Vegas meet-and-greet that must've had Floyd thinking he was seeing double.

Ruby went to the TMT gym on Thursday to watch the champ training for his upcoming fight against Andre Berto. Sources at the gym tell us the "Orange Is the New Black" star said she's been a longtime fan of Floyd's and just really wanted to meet him.

We're told a mutual friend of Floyd and Ruby's doppelganger, Justin Bieber ... helped set up yesterday's meeting.