Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can this even be proved? (Or disproved?)

Any irrational number without a 0 (zero) in its decimal representation is transcendental.

Not sure where to start on this one...

share|improve this question

2 Answers 2

up vote 2 down vote accepted

Wikipedia says,

It has been conjectured that every irrational algebraic number is normal; while no counterexamples are known, there also exists no algebraic number that has been proven to be normal in any base.

share|improve this answer

$\sqrt{6}$ has no zero in its decimal expansion

share|improve this answer
Where do you have that from? If Maple is to be believed, $\sqrt6=2.4494897427831780981972840747058913919659474806567\ldots$ –  Harald Hanche-Olsen May 2 '13 at 8:02
Even if the zero wasn't plainly visible this kind of statement would definitely deserve a justification. Because I certainly have never seen the entire decimal expansion of an irrational number... –  Jim May 2 '13 at 8:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.