On 05/05/2010 12:19 AM, john gilmore wrote:
Ted MacNeil writes:
| BTW, transendental numbers are a subset of irrationals
If, as I think we may safely assume, 'transendental' is a misspelling of
'transcendental', this observation is incorrect.
An irrational number is a non-algebraic real number.
by definition transcendental means non-algebraic.
this applies to real or complex numbers.
An irrational number is a real number that is not rational.
sqrt(2) is an irrational number and algebraic (one solution of x**2=2)
And it is thus perhaps possible to say, very loosely, that real
transcendentals are a subset of the irrationals.
since all rationals are algebraic, i.e. not transcendental ...
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