we have x , y c E with E on the IR espace vectoriel d(x,y) is a distance if the three condition are verified :

1. we take x,y c E ; we have d(x,y)= 0 => x=y the first condition verified

2. we take x,y c E ; we have d(x,y)= |x|+|y| = |y|+|x|= d(y,x) the second condition verified

3. we take x,y,z c E ; we have d(x,z) =|x|+|z| =| |x|+|y|-|y|+|z| | <= |x|+|y|+|y|+|z| <= d(x,y) + d(y,z) the third condition virified

So the d(x,y) is a distance in E So E is an espace metric

Good Luck and if need somthing else tell me

For some reason i did not write the question down! It was actualy show that d does not make a norm ive been having troble proving that

Can you please help me out will rate this quickly after

yes of course ,after how do you find my answer is good ?

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