Roll yer eyes all you want, there are seven continents, and "America" ain't one of them. Quoting from the "History of the Concept" section of the Wiki page on Continent is great for illustrating the evolutionary history of the concept, but it doesn't define what a continent is. It only defines the history of it and how it became what it is today. The historical definition isn't the same as the contemporary definition. There are a lot of terms that are like that. Just because a particular term had one definition in the past doesn't mean that it must retain that same definition for all time. Same as those in some Latin American countries who want to be more closely associated with North America for social and political reasons, so they keep pounding into school children the notion of America being one big continent, and of Spain, Portugal and a couple of other countries trying to hang onto the two Americas being as one continent for their own ego reasons, doesn't make it so.
Most geographers today, to remain consistent with geology and plate tectonics and how the continents actually move, separate North and South America correctly as two distinct land masses, since they are, in fact, two distinct land masses.
Also, you have to be careful relying too much on Wikipedia. For example, the quote from the Olympics PDF that describes the meaning behind the rings, appears nowhere in the PDF itself that was used for the quote.
On the other hand, the first paragraph on that same Wiki page nailed it with
A continent is one of several large landmasses on Earth. They are generally identified by convention rather than any strict criteria, with seven regions commonly regarded as continents – they are (from largest in size to smallest): Asia, Africa, North America, South America, Antarctica, Europe, and Australia.
And of course there several other areas on the same page where it states quite plainly that "America" is not a single continent, but is in fact two continents, each with their own proper name.
Also, while we're at it, saying that America is "not a country" is also somewhat incorrect. While technically "America" is not a country, the accepted nomenclature and practical use of the term is to refer directly to the United States of America. So both in the abstract and the concrete, America is a country. There's a reason why Canadians and Mexicans and Bolivians and Surinamese aren't called Americans, but you can go almost anywhere on the planet and tell people you are an American, and not one of them will instantly think "Brazil", rather, they will know instantly from which country you came.
Truth is...
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America is a country ...... not a continent ......
I'm at a complete loss why that statement, correctly or incorrectly stated, is important enough for a forum sig, tho. For example, your sig, let's say it's a correct statement. OK. My response is, yeah, so? Let's say it's incorrect, which it is, my response it still the same. Yeah, so? If you restate it correctly, as I have done above, my response doesn't change. I must be missing it completely (which shouldn't come as a surprise if I am), but the statement seems to be akin to something like
Velcro is a brand name ...... not a hook and loop enclosure ......
Now there's a statement for the masses.