What is the formal definition of limit?

1 Answer
Wataru
Sep 17, 2014

Precise Definitions

Finite Limit
lim_{x to a}f(x)=L if
for all epsilon>0, there exists delta>0 such that
0<|x-a|< delta Rightarrow |f(x)-L| < epsilon

Infinite Limits
lim_{x to a}f(x)=+infty if
for all M>0, there exists delta>0 such that
0<|x-a|< delta Rightarrow f(x)>M

lim_{x to a}f(x)=-infty if
for all N<0, there exists delta>0 such that
0<|x-a|< delta Rightarrow f(x) < N

Related questions
See all questions in Formal Definition of a Limit at a Point
Impact of this question
4844 views around the world
You can reuse this answer
Creative Commons License