Prove that there is no positive real

[cragar]

Homework Statement

Prove that there exists no smallest positive real number.

The Attempt at a Solution

Lets assume for contradiction that x is the smallest positive real.
Now we will look at the midpoint between 0 and x which is x/2, well x/2 is positive and smaller than x so this is a contradiction, so there is no smallest positive real.

 

[jbunniii]

Looks fine to me. If you want to be pedantic, you may want to prove explicitly that $x/2$ is positive and strictly less than $x$.

 

[micromass]

Depending on how much rigor you need to put in, you might want to prove $0<\frac{x}{2}<x$. I know it's trivial, so perhaps it's not needed.

 

[cragar]

ok thanks, it almost seemed to easy just wanted to make sure it worked.