>And it is thus perhaps possible to say, very loosely, that real >transcendentals are a subset of the irrationals.
It's not loosely! Rational numbers are those that can be described, accurately, as a ratio, ie: fraction. Irrationals are those that cannot. Therefore transcendentals are irrational. But, not all irrational numbers are transendental. The square root of 2, for example is not transendental. It is algebraic: the solution to the equation X*X-2=0. If it is not algebraic, and it is irrational, then it is transcendental. Johann Heinrich Lambert conjectured that e and π were both transcendental numbers in his 1761 paper proving the number π is irrational. >From mathisfun.com: The number e is a famous irrational number, and is one of the most important numbers in mathematics. - Too busy driving to stop for gas! ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to [email protected] with the message: GET IBM-MAIN INFO Search the archives at http://bama.ua.edu/archives/ibm-main.html
