Jesus as Lord - why is this appealing to so many?

[polymath257]

Hilbert's Hotel:

Imagine a hotel with a finite number of rooms. All the rooms are full and a new guest walks in and wants a room. The desk clerk says no rooms are available.

Now imagine a hotel that has an infinite number of rooms. All the rooms are filled up so an infinite number of guests. A new guest walks up and wants a room. All the clerk has to to do is to move the guest in room #1 to room #2 and the guest from #2 to #3 and so on so your new guest can have a room #1. You can do this infinite number of times to a hotel that was already full.

Now imagine instead the clerk moves the guest from #1 to #2 and from #2 to #4 and from #3 to #6 (each being moved to a room number twice the original). All the odd number rooms become vacant. You can add an infinite number of new guests to a hotel that was full and end up with it half empty. 

How many people would be in the hotel if the guest in #1 checked out?

If everyone in odd number rooms checks out, how many checked out? How many are left?

Now what if all the guest above room number 3 check out. How many checked out? How many are left?

So from the above we get:
infinity + infinity = infinity
infinity + infinity = infinity/2
infinity - 1 = infinity
infinity / 2 = infinity
infinity - infinity = 3

Conclusion: the idea of an actual infinite is logically absurd.

The only one of these that is wrong is that last. Subtraction of infinities is not well defined. So yes, we have infinity+3=infinity, but that doesn't mean that infinity-infinity is well defined. In fact, since infinity+5=infinity also, that shows subtraction is NOT well defined.

None of the rest are actual contradictions, are they? They are merely differences between how finite things work and how infinite things work.

Even the fact that subtraction isn't well defined is just one of those differences between finite and infinite collections.

So? Where is the logical absurdity?