Teddy Bloggie Blog Blogging

Today I tutored Pierce on the definition of a limit. You know, it took me about 2 years to understand what the textbooks were trying to tell me. "Who talks like that?" I thought as I tried to understand the mathematical language. It's really more like some intractable legal jargon than what you would imagine straightforward math talk would be. Is it me or does it seem the more precise a language is, the less understandable it actually becomes?

Ok, so you want to specify an Epsilon so that any Delta you choose from X should have you within Epsilon of L. It still sounds confusing, but I'm glad Pierce got it. They really should find a better way of describing a limit than using the old Epsilon and Delta definition. It's like eveyone knows what a limit is, but they have to confuse and torture you with its definition. Where's the cartoon book of limits? Where's the metaphors and analogies that you could use to teach "limits"?

How do you really talk about:
A function f with domain D in R converges to a limit L as x approaches a number c { closure(D) } if:
given any Epsilon > 0 there exists a Delta > 0 such that
if x {D} and | x - c | < Delta, then | f(x) - L | < Epsilon

My personal definition would be something like...
Hey, do you see a line? Does it go to the exact same vertical position when you're approaching it in both horizontal directions? Well, then what you have there is a limit...