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What is δ that they keep refering to in this definition? They first bring it up as if it's some quantity I'm supposed to know... maybe I'm just crazy :)Definition

We call L the limit of f(x) as x approaches [itex]\infty[/itex] if for every number ε > 0 there exists a δ; such that whenever x > δ we have

[tex]\left| f(x) - L \right| < \epsilon[/tex]

When this holds we write

[tex]\lim_{x \to \infty} f(x) = L[/tex]

or

[tex]f(x) \to L \quad as \quad x \to \infty.[/tex]

Similarly, we call L the limit of f(x) as x approaches [itex]-\infty[/itex] if for every number ε > 0, there exists a number δ such that whenever x < δ we have

[tex]\left| f(x) - L \right| < \epsilon[/tex]

When this holds we write

[tex]\lim_{x \to -\infty} f(x) = L[/tex]

or

[tex]f(x) \to L \quad as \quad x \to -\infty.[/tex]

Notice the difference in these two definitions. For the limit of f(x) as x approaches [itex]\infty[/itex] we are interested in those x such that x > δ. For the limit of f(x) as x approaches [itex]-\infty[/itex] we are interested in those x such that x < δ.