Is this following define a metrics?

Question

Is this following define a metrics

$d((x, y), (x’, y’)) = \min\{|x – x’|, |y – y’|\}$ on $\mathbb{R}^2$.

As i found the answer Which of the following define a metric? but not getting in my head

my attempts :i found all the metric properties are satisfies ...im not getting which metric proerpties is no satisfies here ......pliz help me i would be grateful ----any hints or solution will be appreciated

thanks in advances

@G.Sassatelli but that non negativity property hold...if i put x=y=o=x'=y' — , Jan 02 '18 at 14:06
There are three "that" here: the one I have in mind, the one you think you have in mind, and the one you've written. — , Jan 02 '18 at 14:11

score 1 · Answer 1 · answered Jan 02 '18 at 14:08

1

A metric needs $d(z,z') = 0$ if and only if $z = z'$. Can you find an example of $(x,y) \neq (x',y')$ such that the distance is $0$?

answered Jan 02 '18 at 14:08

BallBoy

14,472

thanks a lots Y. Forman – Jan 02 '18 at 14:21

score 0 · Accepted Answer · 2018-01-02T14:10:32.490

0

Put $x=(5,0)$ and $y=(1,0)$. Then $d(x,y)=0$ but $x \neq y$

edited Jan 02 '18 at 14:10

answered Jan 02 '18 at 14:07

Thanks a lot @linkingpark – Jan 02 '18 at 14:22

Is this following define a metrics?

2 Answers2