Actual Infinity in Reality?

[GrandizerII]

About the seeming contradictions in Hilbert's Hotel, here's to put things in clearer perspective:


inf(1,2,3,4,5,6,7,8,9,10,...) - inf(1,2,3,4,5,6,7,8,9,10...) = 0
In this case, inf(positive integers) - inf(positive integers) = 0
or
inf - inf = 0

inf(1,2,3,4,5,6,7,8,9,10,...) - inf(2,4,6,8,10,...) = inf(1,3,5,7,9,...)
In this case, inf(positive integers) - inf(positive even integers) = inf(positive odd integers)
or
inf - inf = inf

inf(1,2,3,4,5,6,7,8,9,10,...) - inf(4,5,6,7,8,9,10,...) = 3
In this case, inf(positive integers) - inf(positive integers except for 1, 2, and 3) = 3
or
inf - inf = 3


So no contradictions, just different infs we're dealing with.

Also, case 1 proves there is no contradiction (because same collection - same collection is indeed 0).

Either way, without context, that is why inf - inf is indeterminate, much like 0/0 is indeterminate.