Even more pedantic: The United States has been at war with North Korea since June 27, 1950. The war has been in a ceasefire state for a long time, but there has never been a formal peace treaty.
Although a still more pedantic person might point out that there was no formal declaration of war in Korea, so technically it's not a "war" (it was called a "police action").
An even more pedantic person might point out that while various norms (international or internal) might obligate a country to declare war before prosecuting it, the fsct of armed international hostilities is war in international law (though it may not trigger all the effects triggered by a declared war in a states internal law) even if there is no declaration.
That would be a good argument that we were at war in 1950, but it's not a good argument that we've been at war continuously since 1950. If the fact of armed hostilities is war, the fact of no hostilities is peace.
Although a still more pedantic person might point out that there was no formal declaration of war in Korea, so technically it's not a "war" (it was called a "police action").