Question

prove if a/(b+c), then either a/b or a/c

Answer 1

Answer:

My initial answer suggested that this was an axiom - but on reflection :

Assuming that a,b,c are all real numbers (i.e. not complex).

The definition of A > B is that A-B is a positive real number.

Since a>b then a-b is a positive real number (call it x) →→ a-b = x

since b>c then b-c is a positive real number (call it y) →→ b-c = y

So :

a-c = a-(b-y) = a-b + y = x + y

since x & y are positive real numbers we know that x + y is a positive real number.

so we can show that a-c = x + y, and therefore a > c