Prove that the square root of 3 is not rational

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The discussion centers on proving that the square root of 3 is not a rational number. It begins with the definition of a rational number as a fraction p/q, where p and q are integers and q is not zero. The contributor attempts to demonstrate that if the square root of 3 can be expressed as such a fraction, it leads to a contradiction, thus proving its irrationality. Clarifications about mathematical notation and concepts, such as the meaning of ε (element of), are also addressed. Ultimately, the contributor expresses confidence in their understanding of the proof.
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Homework Statement


Show that the square root of 3 is not rational


Homework Equations





The Attempt at a Solution



A number is irrational if χ is not ε. Q=p/q: p, q ε z and q is not=0, z=integers

If p/q: p, q is not ε or q=0, then square 3 is rational. If p=square root of 3 and q is not ε, then the square root of 3 cannot be rational.

Could someone please tell me if this is correct and if not show me what I need to do?

Thank you very much
 
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What is your \epsilon?
Do you know how to show that \sqrt{2} is irrational?
 
x ε is "x is an element of x" Yes, I do.

Thank you very much

Now I know how to do it

Regards
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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