In <[email protected]>, on 05/04/2010 at 10:19 PM, john gilmore <[email protected]> said:
>If, as I think we may safely assume, 'transendental' is a misspelling of >'transcendental', this observation is incorrect. Even a stopped clock is right twice a day. >An irrational number is a non-algebraic real number. That's not even wrong. An irrational number is not a ratio of integers and a transcendental number is not a solution of an algebraic equation with integer coefficients. Whether or not you want to count Gaussian integers as integers, some irrational numbers are algebraic and some are transcendental. Perhaps you meant to say "A real transcendental number is a non-algebraic real number." >And it is thus perhaps possible to say, very loosely, that real >transcendentals are a subset of the irrationals. There's nothing loose about that; it's unambiguous and correct. In <[email protected]>, on 05/04/2010 at 02:24 PM, john gilmore <[email protected]> said: >Numbers like sqrt(2) are irrational, i.e., not expressible as a fraction >having an integer numerator and denominator. Neither e nor pi is expressible as a fraction having an integer numerator and denominator. >Numbers like "pi and e" are transcendental. They are a very different >kettle of fish. See above. >Rational numbers have decimal-fraction representations that are either >terminating or repeating, True, but irrelevant. >In general, contributions to this list are valuable when either 1) the >poster talks about what he knows or 2) asks questions about what he does >not know. Physician, heal thyself. -- Shmuel (Seymour J.) Metz, SysProg and JOAT ISO position; see <http://patriot.net/~shmuel/resume/brief.html> We don't care. We don't have to care, we're Congress. (S877: The Shut up and Eat Your spam act of 2003) ---------------------------------------------------------------------- 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
