Perhaps he was referring to Dumbledore's opinion?

It is the same thing.

In more detail: the underlying principle here is called De Morgan's law. De Morgan's law is our name for the fact that to say that a cat is not both furry and white, is the same as saying that the cat is either not-furry or not-white (or both).

(More generally: the negation of a conjunction (respectively, disjunction) is the disjunction (respectively, conjunction) of the negations.)

Suppose we lived in a world with twenty cats. We could make a statement about all of the cats by saying "The first cat is furry and the second cat is furry and the third cat is furry and [...] and the twentieth cat is furry." But that would take too long; instead we just say, "Every cat is furry." Similarly, instead of "Either the first cat is white or the second cat is white or [...] or the twentieth cat is white," we can say, "There exists a white cat." Thus, the same principles that we use for and-statements ("conjunctions") and or-statements ("disjunctions") can be used on ("quantified") for every-statements and there exists-statements. "There does not exist a winged cat" is the same thing as "For every cat, that cat does not have wings" for the same reason that "It is not the case that either the first cat has wings or the second cat has wings" is the same thing as "The first cat does not have wings and the second cat does not have wings." That's de Morgan's law.

So, suppose there does not exist a person who does not die. De Morgan's law tells us that this is equivalent to saying that for every person, that person does not-not-die. But not-not-dying is the same thing as dying. But this is that which was to be proven.

Thanks for posting this TheatreAddict! I also didn't understand the equation, but didn't even think to ask what it meant.

I learned something new today because of you. :)

Red(x) means "x is red." X = Y in this case means that X and Y are either both true or both false. All x : Bouncy(x) means that everything under consideration is bouncy. Exists x : Fluffy(x) means a fluffy thing exists. The sentence says "if everything dies, then nothing doesn't die" and vice versa. This is http://en.wikipedia.org/wiki/First-order_logic .

edit: And here are the fruits of google: http://math.stackexchange.com/questions/52323/how-do-you-read-this-logical-statement-aloud-and-how-do-you-notate-it-in-symbol

So... Does anyone know of any helpful presentations? My brain likes pictures. This was probably the most helpful thing I've come across on here. I'm 16, not the best at math and complex equations, so this sort of helped a lot of stuff click in my mind. :)

There are definitely approaches to QM that smack of subjective reality ("subjective" describing this one you of the many near-clones of you, one in each possible worlds each quantum mechanical outcome involving you creates, if you believe the MWI the way EY does). However, it is indeed best to stay away from the topic unless you are well versed in it.

The topic of quantum mechanics should probably be avoided, unless you can expect the audience to have taken a course or read a book on quantum mechanics. Long story short, though, the "what if we create our own reality?" debate was indeed revived by quantum mechanics. The debate was then concluded, long ago, because this was science and not a debate club. Objective reality was not overturned.