Tag Archives: mathematics

0.999999…

I’m really, really enjoying my Real Analysis class. My inner math geek has been riding on a cloud of euphoria for the last three weeks, and I finally have a good excuse to play with and learn

LaTeX

, something I’ve wanted to do since I was first introduced to it in my undergraduate calculus classes several years back. I’ve already learned a handful of really cool little algorithms for manually calculating certain number sets that we take for granted because we have calculators that do these things for us now. It’s been a fun ride so far, and I still have about 3.5 months left to jones over all this math-y goodness.

On the very first day of class, our professor ((Bless his heart – he’s not the greatest teacher in the world. He definitely knows his stuff, but he does have some trouble presenting it in a clear manner.)) opened a can of worms that continues to pop up in our analytical operations. He had everyone break up into groups and then wrote a group activity on the board for us to discuss:

bq. Is

0.overline{9} = 1

?

In case you’re a bit rusty on your math notation, that’s a zero and decimal point, followed by 9s _ad infinitum_. My initial gut reaction was to say that no, 0.999999… is _not_ equal to 1, that it’s infinitely close to 1 without ever actually reaching 1. But of course, when you think about that for half a second, you have to wonder how you can ever get infinitely close to something without touching it. I was incorrectly thinking in terms of asymptotes, like the equation

y = frac{1}{x}

, which is a pair of curved lines that _do_ approach the x and y axes without ever touching. But 0.999999… is a _straight line_ when graphed, and not the curved line of the aforementioned equation. And if you graph 0.999999…, you’ll see no discernable difference between it and a graphed line of 1 – because the two are the exact same number. They’re just different ways of writing the same number.

Our prof pointed us at “this math blog”:http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html, where the author has a series of five entries with proofs showing clearing that 0.99999… is equal to 1 – and lots of discussion in the comments about the validity of said proofs. It’s very interesting to read down through everything, even through the trolling comments of naysayers, because the interactions and ensuing discussions turn up a lot of really good mathematical equations and proofs. If you’re interested in this sort of thing, I highly recommend that you check it out and even add Polymathematics to your feed reader. ((There haven’t been any updates since 24 December, but I’m hoping that he’ll come back soon with some more juicy math goodness.))

So, are your eyes all glazed over now? Anyone still with me?

openID, dp.SyntaxHighlighter, and LaTeX

As much as I love my hosted version of WordPress and the power I have to customize it however I see fit, there are some drawbacks to the system that I have yet to be able to hurdle.

  • openID. I’ve wanted to set up an openID server for my blog for quite awhile now. The idea of being able to use my domain to securely log into other websites that use openID, rather than having to hassle with different usernames and passwords, was very appealing to me. However, the technology was initially so new that it was difficult to incorporate openID into WordPress without some hefty file hacking to make it work. Then plugins started coming out, some of which worked better than others. Unfortunately, I’ve never been able to get openID to work here, despite a nice little WordPress plugin that’s supposed to take all the hardship right out of installing it. I suspect that problem lies with inadequate support from my webhost, and all my attempts to contact the plugin’s author have been met with the silent treatment. The plugin itself hasn’t even undergone any changes, additions, or revisions since it was first published, so I suspect that it’s probably no longer being supported. This, then, continues to leave me in an openID black hole until something changes either with my webhost or with a plugin developer that can produce an openID plugin that works so well that almost anyone can use it on any hosting package.
  • dp.SyntaxHighlighter. I work enough with CSS in the occasional WordPress or bbPress theming project that I do like to share snippets of code when the situation demands it. There’s a host of good code sharing plugins out there for WordPress, but the WordPress.com developers have incorporated a syntax highlighting package into the .com blogs that’s really slick. The thing that I like so much about it is that it has a little button that will automatically copy all the code to your clipboard for easy pasting into a text editor. Gone is the need to highlight and copy and then have to manually remove the numbers from the beginning of each line. Unfortunately, dp.SyntaxHighlighter has not yet been bundled as a WordPress plugin, and not being terribly adept yet at coding in PHP, I’m not sure where I’d even start to create a plugin to incorporate it into hosted versions of WordPress. I may try tackling the project here at some point and learn much more, I’m sure, about PHP in the process, but that will have to wait for another time when I don’t have quite so much on my plate. I suspect, though, it’s only a matter of time before else beats me to it.
  • LaTeX. The WordPress.com blogs also have LaTeX installed on them for the uber math geeks. I had a brief introduction to LaTeX when I took Calculus from my father-in-law during my undergraduate education (though I hadn’t yet then met his daughter). I’ve always been somewhat intrigued by coding and markup languages, and LaTeX seemed similar in many ways to HTML and C. The beauty of LaTeX, though, lies in its ability to allow you to easily and attractively put complex mathematical formulas and diagrams on a page. The downside to LaTeX, though, is that the software necessary to make it work is rather complicated to install and somewhat less complicated to use. It’s gotten better in recent iterations, of course, but it’s still somewhat cumbersome to set up. The brains over at WordPress.com actually took the time and effort to make LaTeX work with their blogs and to allow anyone who wants to do so to render LaTeX formulas on their WP.com blogs. There are a couple of plugins that allow you to use LaTeX on hosted versions of WordPress, as well, but they depend heavily on all the LaTeX software being installed on your server. Most webhosts do not have these software packages installed, and it is incredibly difficult, if not impossible, to install these packages yourself or to get tech support to install them for you. So, unfortunately, I have yet to get LaTeX installed on this blog. This does, however, providing a major driving motivation for me to use my “WordPress.com blog”:http://stitzelj.wordpress.com a bit more, especially since I intend to spend some time working my way through my old Calculus textbook (yes, I did keep it) in an attempt to learn Calculus again and learn it better this time. So, I may end up referring you back and forth between the two blogs, at least until I can find a way to get LaTeX installed here.