Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Topic: Proofs that numbers are rational, algebraic, or transcendental.
Replies: 6   Last Post: Apr 3, 2013 2:07 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 418
Registered: 10/7/06
Re: Proofs that numbers are rational, algebraic, or transcendental.
Posted: Apr 3, 2013 1:48 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Apr 3, 5:50 pm, Paul <pepste...@gmail.com> wrote:
> All real numbers are obviously either rational, (algebraic and irrational) or transcendental. So these descriptors partition the reals into three disjoint sets.
> From what I've seen, all the difficult results placing a real number into one of these classes have been of the form "x is transcendental".
> Does anyone know of any non-trivial results which show that a specific number is rational or algebraic?  In other words, does anyone know any non-trivial results (advanced undergraduate or higher) which define a specific x and then prove a statement of the type "x is rational" or "x is algebraic"?

Let S(n) = sum (1 / (pi*k)^n) over 1 <= k < infinity.

For some n, S (n) is proven rational, and for others it isn't. (It is
related to Bernoulli numbers when n is even).

For example, the infinite sum of 1/k^2 is pi^2 / 6, so S (2) = 1/6.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.