Now for a bit of pedantry ... (and dads have a habit of being pedantic in my experience) ...
Your example of an infinite loop is more infinite than mine. (reply #3 refers).
For a start, the trip is going to happen next week (say 7 days hence, or worst case 14);
and one step in the program is the boy being told by his teacher that she would be away (during the schoolday ?);
and another is that he tells his grandfather (that night?)
Hence, (even if all the other on-again-off-again phonecalls happen at best possible efficiency, eg during the "night shift", or maybe lunch breaks, and off the critical path), because there is a limit to the number of days in a school week (try 5, or if you're real keen, 7), then I believe we have just established that infinity = 7 (or maybe 14) as a maximum.
PS When I think about it, the kid has to come home one night to say that it is "on-again", and the next to say it is "off-again". My final offer is that infinity = 7 as an absolute max. (**) Make that 6.
But, to be fair, it is at least a good example of that saying "oh what a tangled web we weave ... "
PS ** Monday night the kid says it is on
Tuesday it is off = 1 cycle
Thu off = 2
Saturday off (Amish school - very diligent) = 3
Sunday on (non-Christian Amish)
Monday off = 4
Wed off = 5
Thu on (and now there is only one day of "next week" available for the trip)
Fri off = 6
Who's gonna believe that the boss is going on a business trip that happens to coincide with a weekend?
ok maybe 7, since everyone in this story seems to be pretty gullible anyway.