Sigh. No, again, that is what AMERICANS have been convinced that "Socialism" means. Even in British English the word has another meaning.
What do YOU mean by Anarchism then? Libertarianism is the belief that the State should only protect people's life and property, and everything else should be arranged by private deals between citizens. I understand that Anarchism is one step beyond that: the belief that the government should simply not exist. Isn't that so?