SOLUTION: Does |n + m| = |n| + |m| for all integers n and m? If so, give some examples. If not, give a counterexample. I would say no, because |6 + (-5)| = |6| + |-5| |1| = |6| + |-

Algebra ->  Absolute-value -> SOLUTION: Does |n + m| = |n| + |m| for all integers n and m? If so, give some examples. If not, give a counterexample. I would say no, because |6 + (-5)| = |6| + |-5| |1| = |6| + |-      Log On


   

Question 352218: Does |n + m| = |n| + |m| for all integers n and m? If so, give some examples. If not, give a counterexample.
I would say no, because
|6 + (-5)| = |6| + |-5|
|1| = |6| + |-5|
1 = 6 + 5
1 = 11
Not sure what to write for a counter example

Found 2 solutions by jim_thompson5910, Fombitz:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct. abs%28n%2Bm%29%3C%3Eabs%28n%29%2Babs%28m%29 in general and you just gave a counterexample.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
What you wrote is a counterexample.
You showed one case where abs%28n%2Bm%29=abs%28n%29%2Babs%28m%29 does not hold.
You only need to show it for one example, which you did.