## Friday, August 15, 2008

### Shopping Can Actually be Fun

Decided to do some last minute back to school shopping. Really all I needed was a new pair of shoes and a few other minor things. The only real thing I needed was shoes, everything else I could have bought once I got back to campus, but why not buy now instead of later.

Since I knew that I needed shoes, the first place we (Ann and I) went was to the shoe section of Sears since I had seen the shoes I wanted there before. The shoes I got were Adidas Samba's, I had actually been wanting a pair for the longest while but never got around to actually buying them. They only came out to be \$42.99, and I just happened to have \$40.00 cash in my wallet, so I ended up putting the other \$2.99 on my credit card, I'm sure that I looked pretty weird.

After buying the shoes we just walked around the mall for a while before deciding that I could actually buy some more cloths. Really a fun experience, trying on everything and getting a good laugh at how ridiculous I looked or how amazing it was. The two things that stick out the most are the pink shirt that Ann wanted me to try on even though I told her that I would not buy it. I must admit though that it didn't look all that bad, however, I stand by my decision to not buy it. Then there was this set of brown shorts with white vertical lines, and another set of brown pants. Both were too big so I didn't have to put up much of a fight as to why I wasn't going to buy them. After all of this I just ended up buying a white button down shirts with grayish vertical stripes/lines.

This might not seem all that interesting to most of you but to the parties in attendance it was quite the memorable day.

## Monday, August 11, 2008

### Time Flies

Last night before going to bed I was talking to one of my friends on AIM. I hadn't spoken to them in a while so most of the conversation was about what we each had been up to for the summer. However, we managed to move to a totally unrelated topic and some of their comments left me just a little depressed. So I did what I normally do when this happens, I end the conversation, put up a witty away message and then go to bed.

Wham! I feel better in the morning and it's like the event never happened. Also when I woke up I was thinking about another math problem (similar to #2 in the previous post). After sitting in bed for a while reflecting on last night's conversation and trying to come up with a proof for this problem, I decided that it was time to go and eat breakfast. Then a few hours later I went over to Ann's.

Well I basically spent all day (well really 10.5 hours) with her. We played Guitar Hero 3, something I have so missed from my days in Holland. I convinced her to start playing on the hard difficulty setting. Things went a lot better for her once she got used to the added button, I think now all she has to work on is "reading" and getting used to the speed. Oh and she also needs to get comfortable with "pull ons and hammer ons". After the Guitar Hero session we went to get lunch at the same place we went for my birthday (Far East Cuisine I think). Then we basically messed around online until dinner.

## Sunday, August 10, 2008

### Extracurricular Affairs

Well by this time I am sure that just about everyone has heard about the John Edwards affair. If not, or you for some reason want to read more about it, just click on the previous link and it will take you to an article in the New York Times. Now I am not supporting this kind of activity but really why would you put something like this out when your family is in the public eye? To me it just seems like something that you would want to keep between yourself and your spouse. Regardless, what was he thinking? He is married and even has children. Luckily his two youngest children are not that old, so the kids they will interact with most of their lives will not remember this, but it will still be one of those "family secrets" you are ashamed of. As for his oldest child (who is at Harvard Law) good luck to her and dealing with this, since you know people will want to talk to her about it and how she feels.

Also this not only hurts him and his family but also a certain democratic candidate who happens to be running for president. It also doesn't help that Edwards chose to endorse Obama and not Hillary Clinton. I am sure that the McCain campaign will you this to their advantage when the time is right.

In any case it seems that democrats seem to take part in "extramarital activities", weather holding office or not. Kennedy, Clinton, and now Edwards, just to name a few. Let's see if (and hopefully not) Obama will keep the tradition good.

## Saturday, August 02, 2008

### solution

This is the solution for problem #1 in my previous post.

Let $\epsilon >0$, since $\{p_n\}$ is a Cauchy sequence there exist an $N_1$ such that if $d(p_n,p_m)<\frac{\epsilon}{2}$ if $n,m>N_1.$ Similarly since a subsequence converges to $p$ we have that $d(p,p_{n_i})<\frac{\epsilon}{2}$ when $n_i>N_2$. Now let $N$ be the larger of $N_1$ and $N_2$.

Now $d(p,p_n)\le d(p,p_{n_i})+d(p_{n_i},p_n)<\epsilon$.

Here is the solution for #2 in my previous post (this one took a little longer for me to think of).

Let $\{p_n\}$ be a sequence in $X$ such that $p_n\in E_n$. Now from properties of $\{E_n\}$ we have that $p_i\in E_j$ for all $j\le i.$ Now let $\epsilon>0$, and since $\displaystyle\lim_{n\to\infty}\text{diam}(E_n)=0$ we have that $d(p_n,p_m)<\epsilon$ for $n,m$ large enough. So $p_n\to p\in X$ since $X$ is complete. Additionally, $p$ is a limit point of each $E_n$, so $p\in E_n \forall n$.