Problem Contest – Problem of the Week – October 7, 2003
Transcendental numbers: Some irrational numbers, like the square root of 2 and the 7/3rds power of 3, are algebraic because they arise as solutions of algebraic equations. Other irrationals, like π are transcendental; they are not roots of algebraic equations over the rational numbers. It is well known that e is a transcendental number between 2 and 3. If a and b are distinct rational numbers, is there always a transcendental number between them?
Submit written solution with justification to John Emerson, Warner 312, before 3:00 on Tuesday, October 14. Or leave them in the Warner mailroom.
Note: Join us at the weekly seminars, usually on Tuesday at 3:00 for refreshments.