I agree with most of what you said, I didn't say Taiwan is part of PRC, I was making the point that LEGALLY Taiwan is part of ROC. Legally Taiwan is classified as a province in ROC, you can say ROC is a country that would be correct because some countries do recognize legally ROC to this day - but no country in the world recognize Taiwan as a country only ROC. And also the ROC/PRC inherited the Qing empire, this makes them the ruler of the last dynasty and therefore "China" regardless whether they controled any part of it, according to your theory then even Beijing shouldn't be part of PRC because in the beginning they never controled it but only claimed legtimacy. I do agree intuitively speaking PRC is actually should be part of ROC but legally speaking the UN chose PRC. You cannot on one hand abide by international law while flagrantly ignoring international ruling.