How to Count Infinity
"Some infinities are bigger than other infinities" - Hazel Grace Lancaster, in "The Fault in Our Stars," by John Green minutephysics is now on Google+ - http://bit.ly/qzEwc6 And facebook...
==========
Today we're going to count infinity. Now counting may seem elementary, like, when we say thatwe have five sheep, what we mean is that we have one sheep for every number from one tofive. And ten sheep means one for every number from one to ten… or two to eleven.So we say that two sets have the same number of things in them, simply if you can drawa line relating every item in one set to something in the other, and vice versa, exactly once.They're partners!It's the same when we say that two plus one equals three, or three doesn't equal four:we're just describing the lines you draw to relate one set of things to another. But eitherway, counting sheep is boring, that is, unless you want to count INFINITELY many sheep.Like, if you had a ...
==========
Today we're going to count infinity. Now counting may seem elementary, like, when we say thatwe have five sheep, what we mean is that we have one sheep for every number from one tofive. And ten sheep means one for every number from one to ten… or two to eleven.So we say that two sets have the same number of things in them, simply if you can drawa line relating every item in one set to something in the other, and vice versa, exactly once.They're partners!It's the same when we say that two plus one equals three, or three doesn't equal four:we're just describing the lines you draw to relate one set of things to another. But eitherway, counting sheep is boring, that is, unless you want to count INFINITELY many sheep.Like, if you had a ...
