Clarity Restored

Extendability and Extensionality are very similar words. They mean very different things: the former that if you ever have any set you can generate another from it; the latter that if two collections have identical members then they themselves are the same.

This was the confusion with my essay. Particularly confusing as in different contexts both were paired (as potential axioms) with two other concepts: Totality and Comprehension respectively, which are not very similar words at all but both mean basically the same thing - that if "some" (starting at zero) things share a common property we can bunch them together as a collection or set. (If you want to know the difference between a set and a collection then you'll have to read my coursework... available on demand after 4pm next Friday, lol! Needless to say, a set is NOT a completed collection.)

At some indeterminate point, possibly inconsistently, I ended up merging the first two things together... ending up last week at a total logical impasse and having to give up writing and get an extension. I got all muddled and, well, there was no way I could find the answer myself in all that mess. Yet, having spoken to my tutor for all of 5 seconds, it was SO CLEAR what was wrong. Duh.

Sometimes we really need people in the know that can speak into our lives. I was well stressed about asking for help but when I did everything was sorted out in an instant. We have to be prepared to listen though and I only was when I got desperate!

This was the answer to so much prayer. Not just that I would be able to get clarity but that I would be able to fully rescue my theories. I liked my essay plan so much, I didn't want it to be wrong but there was just no way, when I broke down every stage into the purest logic known to anally-accurate-mankind, that it could be redeemed. Then, in an instant, all the seeming impossibility was ejected and I was back in the game! There was no hope and then there was loads. It didn't matter that in my mind there was no way back... He just pulled something unexpected and totally unpredictable out of the bag and: Hey presto! Magic. Yet, actually just life.

Always keep in mind that something you don't know about yet could make everything entirely different in an instant.

Lots of other cool things happened this week... but they are a secret!