P/s i need help to prove that every positive real no has a unigue positive square root

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- June 28th 2013, 01:02 AMMondellaReal analysis
P/s i need help to prove that every positive real no has a unigue positive square root

- June 28th 2013, 07:01 AMPlatoRe: Real analysis
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? - June 28th 2013, 12:50 PMLord VoldemortRe: Real analysis
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.

- June 28th 2013, 02:11 PMPlatoRe: Real analysis