 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2016

Paper 1

Apply the <triangle inequality> with a third point $x_k$:
$$
d(x_m,x_k)-d(x_n,x_k)\leq d(x_m,x_n)\leq d(x_m,x_k)+d(x_n,x_k).
$$
Letting $k\to\infty$ gives the desired bounds. Interchanging $m,n$ also gives the sharper symmetric lower bound:
$$
\boxed{|d_m-d_n|\leq d(x_m,x_n)\leq d_m+d_n.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 1 / 11G / b / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 1 / 11G / b / iv / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 1 / 11G / b / iv / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)