- #1
1MileCrash
- 1,342
- 41
Hi all,
I was working on a proof that essentially worked because:
|x-y|+|y-z| >= |x-y+y-z|
I knew this was true because, but I'm looking for a generalization in a way that I could write in a proof.
Can you say that when comparing two expressions of addition/subtraction that are identical except for absolute values, if one has more absolute value symbols, it is always greater (or equal)? But then that would also require me to say something like "it has to be a sum/can't be a "negative absolute value (subtraction).." It's hard to explain.
How would you justify the step I did?
I was working on a proof that essentially worked because:
|x-y|+|y-z| >= |x-y+y-z|
I knew this was true because, but I'm looking for a generalization in a way that I could write in a proof.
Can you say that when comparing two expressions of addition/subtraction that are identical except for absolute values, if one has more absolute value symbols, it is always greater (or equal)? But then that would also require me to say something like "it has to be a sum/can't be a "negative absolute value (subtraction).." It's hard to explain.
How would you justify the step I did?