P/s i need help to prove that every positive real no has a unigue positive square root
Any proof of this depends upon the set of definitions and axioms with the sequence of theorems you have.
Here is a general approach. If prove that if then there is at most one such .
Let . You want to show that and is bounded above.
If you can show those then use the completeness property.
Hint: let . Is it true that
What can you do with that?
Plato, can you explain why this doesn't work? Given distinct real numbers x and y in R, suppose they have the same square root z. By definition, z = sqrt(x) and z=sqrt(y), so we have z^2=x=y which is a contradiction, so two distinct real numbers can not have the same square root.