Another Weekend Looms

Sandi and I spent the evening preparing for company this weekend; each of our mothers will be visiting for the upcoming Bethany dinner. They were able to get a carpool arranged, and we look forward to seeing them tomorrow evening. To celebrate the occasion, I will be making some angel hair pasta with Italian sausage and red bell peppers. On Wednesday, we received a new kennel for Ranger, since he looked rather pitiful if he stood in his old one. I think the old box will actually fit inside his new bed, which I find somewhat amusing.

There really is nothing else to report, so I will take this opportunity to boggle your mind with something I discussed with my Concepts of Mathematics class yesterday. We are discussing a branch of mathematics called set theory, which deals with (get this) sets of objects. We call two sets equivalent if they have the same number of elements. Now think about the set of numbers

{1, 2, 3, 4, ...}
-- mathematicians call this set the natural numbers -- as well as the set of even numbers

{2, 4, 6, 8, ...}.

Which of these sets would you say is larger? Your gut would probably say the natural numbers, since the even numbers are contained within it (that is, the even numbers are a subset of the natural numbers). However, you can pair up each even number with a unique natural number if you divide by two. This implies that the two sets are, in fact, equivalent. So there are just as many even numbers as there are natural numbers. This serves as a lesson of sorts in how we have to be careful when we find ourselves talking about the infinite.

Have a great weekend, everybody!