# Bounds of a function and limits

1. Nov 8, 2007

### javi438

1. The problem statement, all variables and given/known data
A function is decreasing if f(x$$_{1}$$) > f(x$$_{2}$$) whenever x$$_{1}$$ < x$$_{2}$$, and x$$_{1}$$, x$$_{2}$$ $$\epsilon$$ $$\Re$$

a) Show that the set {f(x) : x < a} is bounded below
b) Prove that lim (as x goes to a) f(x) = glb{f(x) : x < a}
(hint: show that for any $$\epsilon$$ > 0, there exists $$\delta$$ > 0 such that f(a - $$\delta$$) < c + $$\epsilon$$

i have no idea where to starttttt ><