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Ok, for a short summary. During the Chinese civil war the communists were soundly beating the nationalists (known as the Kuomintang) by 1949, due to huge popular support and excellent strategies on the part of Mao and his subordinates. By the end, the Kuomintang fled to Taiwan, and when Mao established the PRC, the Kuomintang, which now controlled Taiwan only, claimed all of China as their own. Of course, in retaliation the PRC claimed Taiwan as a part of China. For a few decades the rest of the world recognized Taiwan as the real China until they finally had to recognize the PRC. Until recently the Kuomintang was the dominant political party in Taiwan, and as a result there has been tension between the two ever since.
The KMT also claims all of Mongolia, and parts of Siberia, Tajikistan, and Pakistan as part of China.
Taiwan did not recognize Mongolia until 2003, when a non-KMT party came into power
yo i literally just had salt and vinegar chips the other day. that shit is delicious
really annoying to find vegan ones, so i dont eat them as often as id like
EldritchMayo has it pretty well covered, but this video here explains the relationship between Taiwan and the rest of China pretty well. TL;DR: After the Chinese civil war, the Nationalists had lost everything on the mainland and moved their base of operations over to Taiwan. For various reasons, the CPC just didn't bother with trying to reclaim it and so Taiwan exists as a rump state of what remains of the Republic of China to this day
start by reading up on the Chinese Civil War following the collapse of the Qing in 1911