Algorithms

Hello everyone!

Sorry for missing last week's post.  I was a bit busy graduating.  It shouldn't happen again.

I mentioned back in my first post that one of my interests is algorithm design.  This week, I'd like to talk a bit about what that means.  The word "algorithm" gets thrown around a lot in TV shows, movies, and science journalism, and quite often, it's horribly misused.  So let's define our terms before we go further: an algorithm is a sequence of steps which can be followed to turn one form of data into another.

That's kind of an abstract definition, though, so let's dive in with an example.  Let's say we have a list of numbers, and we'd like to know which is the largest.  How might we go about this?  One way to do this is to just walk through the list and keep track of the largest number we've seen.  So in the list below, we start by saying the is the largest number.  Next, we check the and see that it's larger than , so it's the largest so far.  We then check the and see that it's even larger.  Finally, we see that the isn't larger, so is still the largest we've seen.alg_1

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Real Numbers

Hello everyone!

I said a few weeks back that I'd define the real numbers for you.  That's what I'd like to do today.  Last time I mentioned the real numbers, I said we could think of them as infinite decimals.  That is a useful way to think of them for a lot of purposes, but it doesn't really give us a way to work with them rigorously.

To start with, let's take a few big steps back.  There are a lot of real numbers (uncountably many, in fact), so let's work with something simpler.  Say for the moment all we have is the number .  We could actually go further back than that, but it's not easy to rigorously define , so for now, that's a good start.

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