Show that?: # |x| -|y| le |x-y| #
1 Answer
Feb 12, 2017
We can use the triangle inequality which states that:
# |x+y| le |x| + |y| #
we can write:
# \ \ \ \ \ \ \ x=x-y+y #
# :. |x|=|(x-y)+y| le |(x-y)|+|y|#
# :. |x| le |x-y|+|y|#
# :. |x| -|y| le |x-y| \ \ \ # QED
