Re: Contradicrtion-free mathemattics (The new nonstandard analysis
E. E. Escultura
>A normal number is well-defined because there is a rule for finding every >digit: by chosing it at random from the basic integers.
Is an arbitrary function from N to N thus ``known'', because if I know
the function I know it's value at each number in the domain?
Put another way: show me a particular normal number that violates the
trichotomy law. If the law fails, there are specifc numbers that cause
it to fail. You claim that you ``know'' the digits of a normal number
that makes trichotomy fail, so convince me by telling me what they are.
I bet that whatever example you give me will not actually violate the
trichotomy principle...
I assumed that when you said ``computable or known'' you meant
''computable, which means known, ''. There is no accepted
axiomatization of the term ``known'', and your three axioms make no
attempt to define it. It's no wonder you don't believe there is a
contradiction in your system - you never define what any of your terms
means.
.
