 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-144/2/a/i/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 144 / 2 / a / i / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

A filter on a set

U

on

N

is a nonempty family of subsets of

N

such that:

$\emptyset \in / U$ ;
if $A, B \in U$ , then $A \cap B \in U$ ;
if $A \in U$ and $A \subseteq B \subseteq N$ , then $B \in U$ .

These conditions imply

N \in U

.

 Read the full article

 New to topics? Read the docs here!