1. Sep 29, 2013

### zoxee

Prove by contradiction that a real number that is less than every positive real number cannot be positive

having troubles with this

could someone give me a small hint to get started?

2. Sep 29, 2013

### pasmith

Suppose $x > 0$ is such that every positive real number is greater than or equal to $x$. What then is $x/2$?

3. Sep 29, 2013

### zoxee

I'm sorry but I can't seem to proceed even with this hint :(

4. Sep 29, 2013

### pasmith

Given that $x$ is a positive real number, is $x/2$ a positive real number?

5. Sep 29, 2013

### HallsofIvy

Staff Emeritus
I wouldn't even bother with x/2. Suppose x is positive. Can it then be "less than every positive number"

6. Sep 29, 2013

### Staff: Mentor

Please check your PMs. The PF Rules require that you show some effort before we offer tutorial help.