I am a bit of a nerd, so while I generally use "proof" the way most people use it (that is to mean "evidence sufficient to convince me"), in cases involving science or math, I tend to stick to the more formal use (that is, "a formal series of statements demonstrating a logical progression from accepted axioms to a conclusion").
Axiom 1: If Wikipedia lists all the things, then it lists me. Axiom 1.1: I am a member of the set of all the things.
Axiom 2: If something is listed in Wikipedia, Wikipedia's search function will reveal it. Axiom 2.1: Wikipedia's search function is without flaws.
Wikipedia's search function does not reveal a listing for me, therefore I am not listed in Wikipedia. Since I am not listed in Wikipedia, either I am not a member of the set of all things (contradicting axiom 2.1), Wikipedia's search function does not cover all of Wikipedia's content (contradicting axiom 2 and 2.1), or Wikipedia does not list all things (contradicting axiom 1).
But yeah, I'm generally content to look it up in a few places, maybe go check in person if it's not the other side of the country, and call it a day.
Re: Proving the website is false would be tricky
Axiom 1: If Wikipedia lists all the things, then it lists me.
Axiom 1.1: I am a member of the set of all the things.
Axiom 2: If something is listed in Wikipedia, Wikipedia's search function will reveal it.
Axiom 2.1: Wikipedia's search function is without flaws.
Wikipedia's search function does not reveal a listing for me, therefore I am not listed in Wikipedia. Since I am not listed in Wikipedia, either I am not a member of the set of all things (contradicting axiom 2.1), Wikipedia's search function does not cover all of Wikipedia's content (contradicting axiom 2 and 2.1), or Wikipedia does not list all things (contradicting axiom 1).
But yeah, I'm generally content to look it up in a few places, maybe go check in person if it's not the other side of the country, and call it a day.