Levels of Infinity

One of the things I like about Life of Fred is that the exercises leave a lot of room for control by the user.  Not only can we skip questions; we can take a question and travel down that line of thought as far as we would like to go.


In Butterflies, Dr. Schmidt tells us that the set of whole numbers is infinite.  That was easily reworded to ask (since we're in the "Your Turn to Play" section anyway), "How many whole numbers are there?"  SpiderGirl picked a big number.  Then I added 1.  BatBoy jumped up and responded with an even bigger number.  So I added 1.  BatBoy threw out a VERY big number.  Before I could respond (and I could see she had been thinking while BatBoy was jumping) SpiderGirl blurted out, "They go on forever!"  

She's right, they do go on forever.  The special name for the size of a set that goes on forever is "infinite."  What else is infinite?  The universe!  The jury's still out on that one, but it's possible to have an infinite universe.  Particles that make atoms!  Yes, things can be infinitely small.  Fractions!  Yes... but WAIT.  Are there as many fractions as whole numbers, or are there more of one than the other?


Light bulbs blinked on.  In between every pair of whole numbers are countless fractions to be found!  In fact, there are many levels of infinity.


There is more to discuss about infinity, of course, but that was the amount of "WOW" SpiderGirl and BatBoy could take for the time being.  What an exciting discussion!