Solution: Veritasium’s “How An Infinite Hotel Ran Out Of Room”

Binary numbers solve the problem and allow all of ABBA’s friends to get a room!

Cheers!
Wishbone8121

Veritasium’s video:

Also, I’m mainly uploading on Rumble because YouTube gave me a community strike for reporting the actual truth about the Ukraine-Russia Conflict, and my other subject of reporting, the US Covid Response, is impossible to properly cover on YouTube because it has hired ex-intelligence as its content moderation.

[extravagantpanda]

You're missing one thing, which is a very common mistake for this problem: the AB sequences are all INFINITE. This means that they cannot represent UNIQUE binary integers as an integer (in any base) must contain a finite number of digits. You can find some way to map them to integers (e.g. truncate after N digits), but such a mapping can never be 1-1. Veritasium is correct here, (really it isn't Veritasium who is correct as his video just explains century-old math first worked out by Georg Cantor back in the late 1800s). There's plenty of good material you can find online that explains it better than Veritasium's video or than I can here in a youtube comment.

Also At 5:15, you say that the video was making the claim that "you can never fit one infinite into any type of infinite". This is not what the video claims. The claim is that there exist certain infinite sets that are unable to "fit into" (i.e. are larger than) other infinite sets, the infinite set of infinite binary sequences being just one example as it is provably larger than the set of natural numbers. The first half of the video actually contains several examples of how some infinite sets can "fit into" each other if they are the same size or "cardinality".