Question

Prove
Suppose c is a positive number. The following are equivalent:
a) y-c 14 years ago

Answer 1

so what we knowing again from x ?

Answer 2

I dont think i understand your question.

Answer 3

@iheartducks do you know how absolute value function is defined?
\[|x|\]

Answer 4

the distance from zero?

Answer 5

it's defined as
\[|x|= x \ if \ x\ge0\]
\[|x|= -x \ if \ x<0\]

Answer 6

Let x > y and c > 0.
Then x - y > 0 implies 0 < |x - y| < c
Thus, -c < x - y < c
Again, y - c < x < y + c

Furthermore, |x - y| < c implies -c < x - y < c
But 0 < |x - y| < c and 0 < |x - y| with c > 0
Hence x - y > 0 implies x > y, as required