03-28-2006, 06:19 PM
Hi,
Transcendence has nothing to do with number base. To say that something is transcendental is to say that it is never the zero of a polynomial with coefficients from some field. Pi is transcendental over Q, because it is never the zero of an element of Q[x] (the set of polynomials with rational coefficients). It is not transcendental over R or C, because (x - pi) is an element of R[x] and C[x].
-Lemmy
Pete,Mar 27 2006, 06:32 PM Wrote:No. All bases are isomorphic. Anything done in one can be done in any other. Sometimes a given base is more useful because of the underlying problem (e.g., binary for logic) but most of the time it really doesn't matter. For example, pi is transcendental in all bases (except, of course, base pi ;) ).
Transcendence has nothing to do with number base. To say that something is transcendental is to say that it is never the zero of a polynomial with coefficients from some field. Pi is transcendental over Q, because it is never the zero of an element of Q[x] (the set of polynomials with rational coefficients). It is not transcendental over R or C, because (x - pi) is an element of R[x] and C[x].
-Lemmy