# Help understanding the delta-epsilon definition of a limit!!

• Oct 14th 2008, 02:21 PM
jpatrie
Help understanding the delta-epsilon definition of a limit!!
Quote:

Let f be a function defined on an open interval containing c (except possibly at c) and let L be a real number.
for each real ε > 0 there exists a real δ > 0 such that for all x with 0 < |xc| < δ, we have |f(x) − L| < ε. or, symbolically,
My main confusions are with the symbols used, and what they mean, my textbook for my math course was designed by fresh grad students, and it doesn't really identify what all that stuff mean.

• Oct 14th 2008, 02:57 PM
ziggychick
Quote:

Originally Posted by jpatrie
My main confusions are with the symbols used, and what they mean, my textbook for my math course was designed by fresh grad students, and it doesn't really identify what all that stuff mean.

Epsilons and deltas can be pretty overwhelming when you first experience them. Epsilon (e) and delta (d) are just error bounds. You can think of them as small positive real numbers.

In words, lim (x->c) f(x) = L means for any number x in your interval, the closer x is to c, the closer f(x) will be to L.

Note |x-c| just denotes the distance between x and c, or the absolute value of the difference.

So saying "for any e>0 there exists d>0, any for any x, 0<|x-c|<d -> |f(x)-L|<e" means

For ANY small distance e, if the distance between f(x) and L is less than e, than you can ALWAYS find a d so that the distance between x and c is less than d.

Hope this helps! It easier to explain with pictures.
• Oct 14th 2008, 03:11 PM
mr fantastic
Quote:

Originally Posted by jpatrie
My main confusions are with the symbols used, and what they mean, my textbook for my math course was designed by fresh grad students, and it doesn't really identify what all that stuff mean.