Re: Cantorian pseudomathematics

Han de Bruijn wrote:
> cbrown@xxxxxxxxxxxxxxxxx wrote:
>

<snip>

> > What is your point?
>
> My point is that you don't understand what random means.
>

And yet I gave a definition for random that allows me to answer your
questions. Can you give a definition from which I could deduce your
answers to the questions you posed of me?

If you can't, how can I expect to take your statement "the probability
that a random integer is even is 1/2" as having any particular meaning?

My point is that you have not reciprocated; you have only provided
illustrations; from which one cannot actually determine your answers to
similar questions.

<snip>

> > Do you consider 7 to be a random number? Do you consider (a), (b), or
> > (c) to be random numbers?
>
> Is Pi a random number?

How is the answer to /my/ question regarding /your/ definition of
random to be found in my own answer to this question? I already have
described my definition of random; the answers to the questions you
pose are quite simple to determine from this definition.

Is pi a random number by my definition? No, pi is not a sequence of
elements from some set..

Are the digits of pi a random number by my definition? No, the sequence
of digits in the ecimal expansion of pi, taken as a sequence of
selections from the set [0..9] is a calculatable sequence, and so it is
not random.

> Is sqrt(2) a random number?

Can you now apply the logic of the above example to this example?
Sqrt(2) is not a sequence of random numbers, nor does its decimal
expansion represent a sequence of random selections from [0..9],
because this sequence is computable.

> Are prime numbers random?

Is any given prime number random? No, a prime number is not a sequence
of numbers.

Is the sequence of prime numbers a sequence of random numbers by my
definition? No, the sequence of prime numbers forms a computable
sequence, therefore it is not a random sequence by my definition.

> Are Collatz sequences random?

Do you even know how to apply a definition? After the above examples,
can you apply my definition to predict the answer to this question? If
so, what is your point in asking? If not, what information in my
definition is lacking?

>
> *I* didn't claim to understand what random is. *You* did.

I didn't claim to understand what you mean by random - that's why I'mf
orced to ask.

I claim that in order for /your/ statement "if x is a random selection
from the naturals, then the probability that x is even is 1/2" to be a
statement in mathematics, you must tell me what /you/ mean by "x is a
random selection from the naturals".

That's no different from requiring that the mathematical statement "7
is prime", be backed up by a mathematical definition of "prime", and
why "7" is an example of it.

Do you find my definition of random unclear to apply? Is it the same as
your own? If not, what definition do you imply when you say "something
is a random selection from something else"?

Cheers - Chas

.

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