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.)
I think I’ve heard of the hotel. Will have to look up the Immortal’s Guessing Game–that sounds intriguing.
And… google brings up absolutely nothing!
What do you mean, “Don’t tell my mother or the OHS people”? Just take a photo and launch it into cyber-space for the whole world to see, including a mother whose motto has always been “All care taken, no responsibility accepted!” Good Grief, woman, do you have a death wish, or something? Thank goodness for friends to protect you from yourself!
I hereby absolve myself of any further responsibility!