Tuesday, July 23, 2013

Thinking Beyond Big

Even though I've been thinking about nanotechnology and things that are very small lately, I'm also pondering something at the opposite end of the spectrum. Actually, it's not a thing, but an idea.

What do you know about infinity? While teaching about fractions and decimals I often talk about the density property of numbers, or the idea that there always exists another real number between any two given real numbers. For example, can you name a number between 1 and 2? How about 1.5? Can you now name a number between 1 and 1.5? Sure you can! Let's pick 1.4. Can you name a number between 1.4 and 1.5? No matter what numbers you pick, you can always name a number between them, and you can do this forever.

Can numbers be infinitely big and/or infinitely small? Are there different sets of infinite numbers? These are great questions, and the just the very sort I want kids to ponder as they think about numbers and our system of numeration.

Here are two videos I like that nicely capture these questions and ideas.