“Of course I believe that,” said Williams after powering to a 6-1 6-1 win over Coco Vandeweghe after less than an hour on court. “I think there is a number of players on this tour, a few players who believe that.
“I don’t care about the ranking. I’ve been number one. It’s cool. But my thing is just to be the best player. If that means I’m winning and I’m not number one, that’s fine.”
Her one-sided victory came after sister Venus defeated Bethanie Mattek-Sands in straight sets and young American Sloane Stephens upset Italy’s No. 22 seed Francesca Schiavone.
Williams said she was thriving on her mentoring role with the 19-year-old Stephens.
“She’s a great person and an amazing player,” Williams said.
“She’s playing so smooth. She looks like she gives no effort when she plays. She’s such a beautiful, beautiful player and yes, I embrace that.
“I hope I can teach her some things. We can feed off each other. She can teach me a few things – maybe how to be calm on the court.”