Hilbert was the world’s best and most influential mathematician from roughly 1890-1920. He did too much for me to reasonably summarize, so I’ll just post this cool video on the Hilbert Hotel, in which he explained a concept discovered by Cantor.
Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
It’s undefined. Here’s why: Suppose A is the set of all positive integers, B is the set of all positive even integers, and C is the set of all positive integers greater than or equal to 3. Each of A, B, C are infinite sets. But A-B (meaning, what’s left when you remove B from A) is the set of all positive odd integers, an infinite set. On the other hand, A-C is equal to the set {1,2}, which has cardinality 2, finite. You can’t get a definite answer, so it’s undefined.I mean, how much is ∞ - ∞ ?
So how does Hilbert reconcile this with his hotel? The Hotel California Corundum: an infinite set can check in anytime they'd like but it's not clear whether they can ever leave?It’s undefined. Here’s why: Suppose A is the set of all positive integers, B is the set of all positive even integers, and C is the set of all positive integers greater than or equal to 3. Each of A, B, C are infinite sets. But A-B (meaning, what’s left when you remove B from A) is the set of all positive odd integers, an infinite set. On the other hand, A-C is equal to the set {1,2}, which has cardinality 2, finite. You can’t get a definite answer, so it’s undefined.
It’s undefined. Here’s why: Suppose A is the set of all positive integers, B is the set of all positive even integers, and C is the set of all positive integers greater than or equal to 3. Each of A, B, C are infinite sets. But A-B (meaning, what’s left when you remove B from A) is the set of all positive odd integers, an infinite set. On the other hand, A-C is equal to the set {1,2}, which has cardinality 2, finite. You can’t get a definite answer, so it’s undefined.
An infinite number can leave the hotel at any time. It’s just that after an infinite number of guests check out, there’s no certainty as to how many guests remain.So how does Hilbert reconcile this with his hotel? The Hotel California Corundum: an infinite set can check in anytime they'd like but it's not clear whether they can ever leave?
Hilbert’s Hotel is easier to explain.I liked Schrodinger's Cat better.
But Schrodinger's Cat has a cat. So...Hilbert’s Hotel is easier to explain.
Must be at a Dollar General, the store for people that can’t do math. Everything is cheaper there.......but every is in smaller packages. So you pay more per oz, qt, unit of whatever you’re buying.
Hmmm, what if that bus came by, empty this time, and an infinite number of hotel guests check out of the hotel? Will there still be an infinite number of guests in the hotel or will it be empty? I mean, how much is ∞ - ∞ ?
Zero, just as one - one = zero!
So infinity is actually like the rats in NYC (or DC). Until you catch them, they don't exist?No.
one - one = 0, two - two = 0, three - three = 0, ..., but ∞ - ∞ is undefined.
See LionJim's explanations why.
I liked Schrodinger's Cat better.
To me, a show that should have been cancelled years ago (is it still on?)...
To me, a show that should have been cancelled years ago (is it still on?)...
Penny does make things better though. She was Jon Ritter's daughter in a sit-com if I recall.
I liked Schrodinger's Cat better.
Plus, cats are tough mother ****ers. Give them 5% points just for that, right?It has always fascinated me.
But what I always wondered was, wouldn’t the cat itself be an observer — one that would sure as hell know whether it was still alive or not — and thus collapse the wave function of that potentially decaying atomic particle that would release the poison, meaning that there would be a definite result inside the box even before the experimenter opened it up to look?
Plus, cats are tough mother ****ers. Give them 5% points just for that, right?
Hilbert was the world’s best and most influential mathematician from roughly 1890-1920. He did too much for me to reasonably summarize, so I’ll just post this cool video on the Hilbert Hotel, in which he explained a concept discovered by Cantor.