You can tell if a mainlander really considers Taiwan a part of China by their reaction to Taiwan sports winsTaiwan scores historic basketball win over China
Back in 2013, theRepublic of China (Taiwan) defeated mainland China in basketball. Many of my mainland co-worker friends were quite shocked and felt defeated. But I was there to reminded them:
"Hey, Taiwan is a part of China, you should be happy that China won the Asian championship!"
As someone of Chinese ancestry who grew up in the US I like seeing the Republic of China and People's Republic of China alike do well in sports (and as an Asian-American, any Asian country really). But on to more political matters...
It's perfectly normal for there to be multiple feuding dynasties of 'China' in China
China, China, and China fight for supremacy in China
Whenever a mainlander or Taiwanese asks me my thoughts on "is Taiwan a part of China", I just ask them what their favorite three kingdoms leader is. Then we go eat Chinese food (such as KFC) and peace is maintained for yet another day.