Tag Archives: Irrational numbers

Existence of a real number such that when added to seq of real gives all irrationals

Posted on January 27, 2015 by Sumant Sumant

Let be arbitrary real numbers. Prove that there exists a real number such that each of the numbers is irrational. It’s easy to see that if all are rational numbers then any irrational number will do the job because the … Continue reading →

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Beatty’s Theorem

Posted on January 23, 2015 by Sumant Sumant

In 1926, Sam Beatty of the University of Toronto made a remarkable discovery concerning sequences of irrational numbers. For a given irrational number and . The sequence and is a complementary sequence. Proof: We see that Since is Integer, we … Continue reading →

Posted in Famous Problem, Number Theory, Sequences | Tagged , | Leave a comment