Wrong Axiom?

Consider this:

Given that

1+x > 2-y ...........(1)

where {x,y} is between {0..1},

intuitively the statement can be rewritten in equality as

1+x+z = 2-y ...........(2)

where z is some constant satisfying 0 < z < 1. Now, rearranging (2) we have

x+y+z = 2-1
x+y+z = 1 ...............(3)

Since z is a constant, the only variables are x and y.

1. Now, pick an arbitrary x and y satisfying condition (1) and assume z constant, and apply the same x and y to (3). Statements (1) and (3) does not agree.

2. Now, pick an arbitrary x and y satisfying condition (3) and assume z constant, and apply the same x and y to (1). Statement (3) and (1) does not agree as well.

Conclusion:

The axiom 'K > M can be written as (K+x)=M' fails for {K,M} between {0..1}

-::TheNewAgeThinker::-