Day 2 of School

So these are from Wednesday.  I was just too tired to try to type it up sooner.  It rained on Wednesday, and I wasn't paying attention and I cut my thumb open on my umbrella - and had to get it glued together so it would stop bleeding.  Don't ask.  I must be special to cut my thumb open that good on an umbrella.

More from my Topology prof...

Most of math is working hard to write the correct definition.  If you can define something properly, then everything else just works out fine.  So if there is an issue with your definition, just add or subtract things until it works the way you want.  (My mother would say that sounds an awful lot like cheating!)

Another gem:  "You will learn to do proofs by doing proofs."  Hm.  Or maybe you could teach us?

The prof told us that all of math can be boiled down to about 20 examples and they can work for everything.  When he started teaching, it would take him half a class period to cover an example.  Not he says he can do it in 5 minutes, but he isn't sure anyone understands it!
Cantor Set Example
So he puts this example on the board.  This is a Cantor Set.  You start with a bar of length equal to 1.  Then you remove the middle third (the piece between 1/3 and 2/3), so that you have one black bar, a white space, and another black bar.  In the third row, for each of the black bars, you again remove the middle third.  You continue this process, until as my professor proclaims, you get DUST (complete with sound effects!).  The 'mathematical definition' of dust:  all the remaining pieces are completely disconnected.  (See there is that definition thing again!)  He then goes on to say that we don't know what connected means, so saying it is disconnected is not meaningful in any way, but he is pretty sure we will get to covering that in about 5 weeks!
Another fun fact about this....  If you add up all the white bars, the pieces that were removed, it adds up to 1!  Which doesn't make any sense because you still have some 'dust' left at the end.  I see how it mathematically works out that way.  It has to do with as things go to infinity, but still, a bit hard to wrap your mind around!

What we are doing in this class is like the CDC, when they have the virus in a box and they use those thick gloves to work with it.  We have stuck topology in a box so you could work with it.  (Say what?)

The topologies, we abbreviate with the letter T (with some squiggleys in it).  However, he wrote them with J for half the class period, and then he was like, you know, something is not right about that.  He stares at his notes for the LONGEST time and he is like - I don't know what letter that should be, I don't have any idea what my notes say!

Last, but not least, he tells a story in class about countries where pubs are forbidden.  So he says you go to the grocery store, decide what size bottle of alcohol you want to purchase, and then you stand in the aisle with your hand in front of your chest holding up the number of fingers for the number of people you want to share it with.  So maybe 3 people.  One person stops and waits with you, so then you hold up 2 fingers.  Once you get your 3 people, the 4 of you proceed to the checkstand and purchase the alcohol.  Then you go outside and sit somewhere and enjoy it together.  He said it really ends up being a lot like a pub because you go there and drink with strangers anyway, so it isn't any different.  (I have no idea why he told this story, but it was pretty funny!)