Re: Contradicrtion-free mathemattics (The new nonstandard analysis
>7) A real number is normal if every digit can be determined by choosing a digit from the basic
>integers, 0, 1, ..., 9, at random. Let x be a real number and y a normal number. While every digit of y
>can be determined or computed and is, therefore, well-defined, it IS not known if x < y or x = y
>or x > y. This is a counterexample to the trichotomy axiom.
You contradict your definition that your ``real numbers'' are
computable decimal expansions. No computable decimal expansion is
normal in the sense you describe.
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To be precise, let me now consistently refer to my real numbers as decimals.
A normal number is well-defined because there is a rule for finding every digit: by chosing it at random from the basic integers. I do not mean expansion but choosing each digit.
Cheers
E. E. escultura
.
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