# Proof by contradiction

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?

## Answers and Replies

pasmith
Homework Helper
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?

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

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

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

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

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

HallsofIvy
Science Advisor
Homework Helper
I wouldn't even bother with x/2. Suppose x is positive. Can it then be "less than every positive number"

berkeman
Mentor
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?

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