Taiwan Is a Part of China, Says Pink Floyd's Roger Waters
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There is not free travel between the two, they both have independent militaries, they both have foreign representatives. In fact it is harder for PRC Chinese to visit Taiwan than most other countries (they require even a special passport/visa for PRC to go to Taiwan).
Whatever your view on whether Taiwan SHOULD be part of China, it is by EVERY objective measure, NOT part of china. The main mark against that, is it is not officially recognised by the UN.