 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ib/paper-3/12f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

(f_{n})

f

A

when, for every

ε > 0

, there is

N

such that

n \geq N ⟹ ∣ f_{n} (x) - f (x) ∣ < ε

for every

x \in A

f

is uniformly continuous when, for every

ε > 0

, there is

δ > 0

such that

x, y \in A

and

∥ x - y ∥ < δ

imply

∣ f (x) - f (y) ∣ < ε

. The same

δ

works throughout the domain.

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