Very far :P
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UN forces went all the way to the Yalu River (the border between North Korea and China). Had China not jumped in, there would not be a divided penninsula today.
North Korea
North Korea
The US Government supported the Korean War.
South Korea
The Korean War (Korean Conflict)
Joseph Stalin supported the North Korean attack in South Korea. Without his support there would have been no Korean War, as we know it today. The Korean War was a US-Soviet War fought by proxy. When Stalin died in 1953, the Korean War ended (1953).
The nations that were involved in the Korean war were the US who aided south Korea and the soviet union, who aided north Korea.
The US never declared war on North Korea. The Korean War was between the United Nations and North Korea, (assisted by Russia and China).
The US reinforced the South Koreans and fought northward into North Korea.
North Korea/Red China vs US/UN.
North Korea was believed to have received war materials from Russia and Russian pilot were believed to have flown North Korean jet fighters against US forces
The Korean War directly resulted in the US NOT INVADING North Vietnam.