Thursday, February 05, 2009
Ed commented the other day that "never" is a good substitute for "infinity" in thinking. I had never thought of that before, and I think it's a very neat idea.
You can apply it to my previous post. Are you skeptical that two parallel lines meet at a "point at infinity"? What if we say, instead, that they meet "never." Sounds pretty good.
Similarly, the value of the function y = 5 - 1/x (graph at left) approaches 5 as x approaches positive infinity. When does it reach 5? "Never."
See how that works?