MAT 2122

Pre Midterm One

What is an open Ball

Let a ∈ R^n, ε > 0, Bε (a) = {x ∈ R^n | ||x - a|| < ε}

What is an open set

A set A ⊂ R^n is open if ∀ a ∈ A, ∃ ε>0 s.t Bε(a) ⊆ A

What is a Boundary

Let A ⊆ R^n, Boundary of A is {a ∈ R^n | ∀ ε > 0, Bε(a) intersects both A and its complement.}

Limit Definition

A function f: R -> R has a limit L as x approaches c if for every ε > 0, there exists a δ > 0 such that |f(x) - L| < ε whenever 0 < |x - c| < δ.