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Mathematics and Infinity

Mathematics and the Infinite
Kurt Owen, Middle & Upper School Science & Math Teacher
  • Blog: Consider This... Mathematics and the Infinite

As a math teacher, I have noticed how uncomfortable students are with the concept of infinity. Most young children, when they first learn of infinity, mistake it for the trump card of all numbers. They like to tout their knowledge by saying, "Give me the biggest number that you can think of." After some paltry number like one billion is thrown out, they reply, "Aha, infinity is even bigger!"

When students become a little more mature, they realize that infinity is really just a direction on the line of numbers. It says to simply keep going, the end will never be in sight.

Then, when they grow a little more, students are able to wrestle with the idea that a discrete whole can divide down into infinitely small pieces. Just when you think that you have sliced something down into the tiniest amount possible, you can make it even thinner. You can take an infinite number of half steps between two points that are separated by inches.

Our understanding of the infinite never really reaches a conclusion. There is always a little more around the next corner. I think that this is a wonderful reflection on our Creator. We may want God to be very predictable like the counting numbers. At other times, we may want God to have a discrete answer for us, like the problem 2x - 7 = 3. (The answer is x = 5.) But God is taking us on a journey, where limits do not fully exist, and more is hidden in every moment than we can ever realize. Where exactly does 2^x = x, anyway?