NK did not accept the stalemate that the Korean War ended in; and denied peace. Therefore, we are technically still at war, yes. Practicall speaking, however, the war was over to the rest of the world. That said, would current administration decide to exercise military force against NK, it would technically not need a declaration of war.
Until military force is actually implemented, though, that doesn't really mean a whole lot from a practical perspective.
North Korea is constructing components for nuclear bombs and has claimed to detonate a hydrogen bomb. The military power involved shows that North Korea is getting ready for a massive war. And, just about a month ago, a U.S. plane flew over South Korea to assure them that they would stand with them. Both North and South Korea are still technically at war; it's only a matter of time before it becomes an official cold war.
The Chinese are still obligated to fight for North Korea, and the United States is still obligated to fight for South Korea. In all probability this is where WW3 will start. It is confounding to think that a hermit kingdom run by a 30 something mass murderer could bring the whole world to war, but it is very possible.
Yes, the U.S. and DPRK are still by all means at war. While not actively engaged in battle, if either of the two countries decide to begin fighting again, the battle will continue. The U.S. would not need a declaration of war from congress to strike the DPRK as war has already been declared and never resolved. More likely, either China will cease support of the DPRK causing famine, disease and death leading to a treaty or DPRK will escalate even further militaristic tensions between themselves and the ROK, US and Japan, leading to reignition of military conflict. Neither of which is horribly unlikely, with DPRK denouncing the armistice and bolstering its nuclear arms status as well as more and more frequent provocative rhetoric.
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Yes, North Korea is still at war with the Untied States, because we technically never ended the war. There are still guards stationed at the border, because we never signed a peace agreement. We signed a cease fire, but that is not the same thing. We should go back and liberate the people up North.
North Korea is still at war with the United States. The current leader of North Korea carries the vengeance of his father from the original Korean War to this day. He makes threatening remarks towards the United States and also exemplifies his hatred for Western democracy by the violent acts he commits.
North Korea is still at way with the United States, when speaking in literal terms. The Korean War was never actually ended, there is only a cease-fire agreement. This is why we still have a guarded line and why the tensions remain so high. Hopefully, one day in the future, it can be ended in an amicable way, but thus far its been impossible.
North Korea is technically still at war with the United States. Although the two states agreed to a cease fire at the end of the Korean war, there was never an official peace treaty. It is likely that the hostilities will continue in the future since both countries cannot agree to come to peace.
It is a well-known fact that the DPRK and the ROK are still technically at war. That is made known with the occasional and unfortunate skirmishes that still happen along their disputed borders (mostly at sea). There is a reasonable question to ask though that this opinion debate asks "is the United States still at war with North Korea?" The technical answer is "yes".
Just like how the DPRK and the ROK signed an armistice ending open conflict and setting up a DMZ; the United States also only signed an armistice with the DPRK. An armistice is not a peace treaty by any means and is often intended to be temporary. An armistice only ends open conflict and sets up rules to instate reasonable peace among the involved parties for the time being. An armistice can also be called a "truce". Until the United States sign a peace treaty with the DPRK (unlikely in foreseeable future) we will be, technically, at war.
North Korea are not at war with the United States, and if they were to start a war with the United States, it would be over in a matter of seconds - literal seconds. There's no real definitive proof of their nuclear capabilities, and at this point they're resigned to occasionally firing shells at South Korea as impotent shows of aggression. The truth is, they're far too destitute to actually compete on any military level. They'll destroy themselves.