i've juste asked myself if it is possible to proof that there is no rational number such that $x^2=3$ using rational sequence. I know that there is a more direct maneer to proof this assertion but i'd like to know if it is possible to show with sequences. I was thinking to try to proof by absurd and show then that the left and right limit are not equal. Thanks in advance!
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1Does this answer your question? How to prove that $\sqrt 3$ is an irrational number?. See Aryabhata's proof using continued fractions. – Dietrich Burde Dec 06 '20 at 15:05
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I don't see how you want to define your sequences. Can you elaborate on that? – Severin Schraven Dec 06 '20 at 15:05