In the course of proving that [itex] \sqrt{3} [/itex] is irrational, I had another question pop up. To prove that [itex] \sqrt{3} [/itex] is irrational, I first assumed 2 things: [itex] \sqrt{3}[/itex] is rational, and the rational form of [itex] \sqrt{3} [/itex] is in it's lowest form. I then broke the proof up into cases and showed that none of these cases could occur.(adsbygoogle = window.adsbygoogle || []).push({});

My question boils down to: did I actually show that [itex] \sqrt{3} [/itex] is irrational?

From a purely logical standpoint, let's say that the 2 assumptions I made were named A and B. I successfully showed that A [itex] \wedge [/itex] B is false. However, this doesn't mean that BOTH A and B are false. More specifically, A could be true and B could be false, and I would still arrive at A [itex] \wedge [/itex] B being false.

On the other hand, the second assumption that was made (the rational form of [itex] \sqrt{3} [/itex] is in it's lowest form) shouldn't (doesn't?) change the problem.

Could someone give me solace and explain this little technicality I have? Thank you very much!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Falsity of assumptions question.

**Physics Forums | Science Articles, Homework Help, Discussion**