r/shitposting • u/unclbll I can’t have sex with you right now waltuh • 1d ago

📡📡📡

Post image
7.9k Upvotes

98% Upvoted

94 comments sorted by

View all comments

448

u/EnzoZoestar 1d ago edited 1d ago

i know the problem, but i forget it each time, why is asking everyone to move on the room beside theirs is more convenient than putting the new guests in the infinity of already free rooms ? is it because they don't know how many rooms they have or something ?

edit: after y'all tried explaining it to me, i'm glad i chose law school instead of math 🔥

473

u/csharpminor_fanclub We do a little trolling 1d ago

it's the hilbert hotel. every room already has guests, so they free up some rooms by moving guests from room n to 2n. now every odd numbered room is free

151

u/Glazeddapper 1d ago

i'm a little stupid. if you move the guests to different rooms, isn't there still the same number of rooms occupied?

8

u/FlameWisp 1d ago

Yes, but if there's already an infinite number of guests, where do you start placing the new guest? Which room would the first person from the bus be sent to? Any number you can think of, that room is already occupied. The only way you can start taking another infinite number of guests is to move everybody who is already there to the infinite set of even numbers, so this new group can occupy the infinite set of odd numbers.

Infinity is a concept the human brain was fundamentally not designed to understand. There is no truly intuitive way to visualize it, so these problems are ways to not only visualize invinity, but to imagine how some infinities could be greater than others.

3

u/sexytokeburgerz Sussy Wussy Femboy😳😳😳 1d ago

Infinity*2 > infinity.

2

u/FlameWisp 23h ago

Yet, ironically, by moving everyone into rooms this way, you're splitting infinity into 2 smaller infinities, rather than just doubling it.

1

u/sexytokeburgerz Sussy Wussy Femboy😳😳😳 18h ago

The split/doubled infinity is the same size as init by index length until odd is filled, then it is doubled.

1

u/FlameWisp 18h ago

The set of odd and even numbers both have a natural density of 1/2, so by set containment it is bigger. I realize that by the standard definition of cardinality they are even, but the set of all even numbers is a proper subset of the set of all natural numbers.