Aleph-nought “To Do” lists

Mathematicians have a concept called aleph-nought. It’s for counting a certain kind of infinite set. Just as “4” is the number name for the number of asterisks in the set {****}, “aleph-nought” is the number name for the number of asterisks in the set {********…}, where the … is meant to indicate that the asterisks go on forever. You can start counting this set in the usual way — 1, 2, 3, 4, 5, 6, … — but the point is that you will have to keep on going without stopping.

Sets with cardinality aleph-nought have some really cool properties. You can add a few more things and the number of things all together is still aleph-nought (this is one of the things that makes the kiddy quote “infinity plus 1” kind of amusing). You can actually add aleph-nought number of things and you’ve still only got aleph-nought of them (which freaks kids out when you try to explain that they can’t beat you with “infinity plus infinity”).

You can also remove a few things from a set of size aleph-nought without making it any smaller.

This brings me to my “To Do” list. I have decided that it must be of size aleph-nought. I cross things off and it doesn’t get any smaller.

The REALLY scary thing, is that it is possible to remove aleph-nought things from a set of size aleph-nought and still have aleph-nought remaining*.

I am doomed.

* * * * *
(This is a break in the blog entry, not a set of size 5!!

Note to self: What fool didn’t anticipate that grand final day would mean that she couldn’t even make contact with a taxi company let alone find a cab to the airport? At moments like this you need Minties (actually, I really don’t like Minties) and very helpful friends (I really do like my friends; they’re much more useful than Minties). Thanks John! (Getting to the airport became one of today’s “six impossible things” … although I didn’t accomplish the suitcase one as well as I would like, and you know what happened to the To Do list … and there are two I can’t account for.)

* I should point out — to round out tonight’s maths lesson — that it is also possible to remove a set of size aleph-nought from a set of size aleph-nought and leave nothing … or 2 items … or 100 items ……… depending on what set of things you remove. Examples for all these claims can be supplied on request. (Go on: I dare you! And ask about Hilbert’s Hotel as well, while you’re at it! AND the “Immortal’s Guessing Game”. Alternatively come back here in a couple of days and I’ll have a link to some stuff I wrote a while ago, which is too messy for me to get on-line in the next half-hour of being stuck in the Qantas lounge.)