 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-ii/2/a/i/solution

(a_{n})

ℓ

when

\forall ε > 0 \exists N \in N \forall n \geq N : ∣ a_{n} - ℓ ∣ < ε .

\forall M \in R \exists N \in N \forall n \geq N : a_{n} > M .

In both definitions the same

N

must control every later term. The second condition is not convergence to a real number.

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