Re:Flaw of Averages (2002)
by xboxnolifes on Tuesday January 04, 2022 @02:30PM
(#29798976)
> But not all of them are populated; therefore only a finite number are.
Isn't this a leap in logic? Not all subsets of an infinite set are finite.
How do you mean that not all subsets of an infinite set are finite, or in what cases would this be so?
Take all the even numbers. That's a subset of all whole numbers. Is it a finite set? Clearly not. Both are infinite; the population of even numbers is 50%. Sometimes infinity/infinity = 0.5.
The set of prime integers is a strict subset of the set of integers, and yet both are infinite (they have the same cardinality even--that is, they are the same size, in one sense of 'size').
Re:Flaw of Averages (2002)
by xboxnolifes on Tuesday January 04, 2022 @04:03PM
(#29800479)
Ex: {n ∈ R ∣ n is odd}
The universe isn't infinite either. But neither of those is the major error with his reasoning.
Re:Flaw of Averages (2002)
by AnimalMuppet on Tuesday January 04, 2022 @02:55PM
(#29799395)
Douglas Adams wasn't writing a treatise on mathematics...
Re:Flaw of Averages (2002)
by xboxnolifes on Tuesday January 04, 2022 @04:09PM
(#29800556)
He was not, but the usage of the quote in this context implies some relevance to mathematical averaging and it's flaws. If the reasoning is not sound, neither is the usefulness in this context.
"Population: None. Although you might see people from time to time, they are most likely products of your imagination. Simple mathematics tells us that the population of the Universe must be zero. Why? Well given that the volume of the universe is infinite there must be an infinite number of worlds. But not all of them are populated; therefore only a finite number are. Any finite number divided by infinity is zero, therefore the average population of the Universe is zero, and so the total population must be zero."