Infinity is forever, you could count for ever and never reach infinity. There are various types of infinity and this presentation will explain some described in the television programme, ‘The Hotel Hilbert’.

What is infinity?

The Hotel Hilbert is an infinite hotel, meaning it is and can cater for infinity in many aspects.

For instance its corridors each have an infinite number of rooms, there is also an infinite number of corridors as well.

So the hotel will always have vacancies for new guests, the current residents all move up one room down the corridor.

Structure of The Hotel Hilbert

The hotel often receives an infinite amount of new guests, therefore all current guests move to an even number room, this leaves an infinite amount of odd rooms for the new arrivals.

Running an Infinite HotelAs you can imagine running an infinite hotel would be hard to say the least.

For example the porter needs to deliver newspapers to every room, so to do this you must zigzag the corridors (as shown below) or else only one half will ever receive theirs.

1 3 5 7 9 11 13 15 17 19

2 4 6 8 10 12 14 16 18 20

Or imagine you are competing with an infinite number of infinite hotels, and suddenly an infinite number close and each has an infinite number of guests requiring an infinite number of rooms per infinite hotel.

Coping with InfinityNow in the example above an infinite number of people need rooms, easy each corridor is infinite right? Well yes but when an infinite number of guests arrive its okay but Infinity-Infinity=0, so suddenly there is a problem. Luckily we own an infinite hotel with an infinite number of corridors.

X InfinitySo now every new guest has a room, but wait what about the current guests. Well infinity has a solution once again, each guest needs to double up their corridor leaving an infinite number free (1 goes to 2, 2 to 4…etc, leaving 3,5,6,7,…etc free), therefore problem solved.

Things to do at The Hotel Hilbert

The Hotel Hilbert has a number of ways to pass time but of course all feature infinity.

For instance the hotel has a wonderful bar serving a variety of drinks with every refill +1. Or check out the restaurant with an infinite selection of infinite choices with infinite combinations available. But be careful an infinite combination may take a long time to prepare…. Maybe even infinity!

Want some fun? The Hotel Hilbert is located next to a beautiful beach with an excellent view and daily games are held on the beach, I hope you enjoy infinite games.

An Infinite game?Infinite games are really just normal games just thought of from a different perspective. The Hotel Hilbert prides itself with an excellent version of infinite archery.

50m

25m

12.5m

6.25m

As shown above the concept of infinite archery. The arrow flies 50m but first it flies 25m, then 12.5m then 6.25m and so on. According to this series the object will reach its target in infinity, so according to this motion is impossible, ‘but we can move’ you might say. Which is true, but we’re not thinking about it! This is known as Xeno’s paradox.

All Infinities are the same?Aside from obvious differences all infinities seem the same.

For example; Infinity + Infinity = Infinity also: Infinity x Infinity = Infinity

So all infinities are the same? Wrong not all infinities are the same, there are even infinities The Hotel Hilbert cannot accommodate for. Take the menu for example, there is an infinite selection of choices so if every guest in the hotel ordered a different selection, there would have been every selection chosen (Infinity – Infinity = 0) but as there are an infinite number of combinations every guest can have a different choice and there would still be different combinations left to try.

What is infinity?During your stay at The Hotel Hilbert you will experience just a few of an infinite number of infinities.

But remember infinity is not a large number there are not an infinite number of grains of sand, in time they could all be counted, along time but not infinity. Infinity is forever and even then is never reached as time is not known to be infinite.

So when coming to stay at The Hotel Hilbert everything is infinite including the length of your stay. You can't leave as this would leave a gap in infinity which will never be filled. Enjoy your stay at The Hotel Hilbert it could take forever…….!