Re: definition of statistical test for randomness

"asdf" <qjohnny2000@xxxxxxxxx> wrote in message
Is there such a thing as a "valid" test for non-randomness - a
test that can be used to give you confidence.

No there isn't. The reason is very simple, in a true balanced coin flip
are just as likely to have
or any other pattern so no test on the output can ever test for

- Suppose though that these 0's went on forever - then you could say
the string was not random.

No you couldn't, it is still a perfectly valid output from a random bit

- But if the number of 0's went above the number or 1's and below the
number of 1's an infinite amount
of times I'm not sure if this says the sequence is not random.

It means nothing compared to a perfect random bit generator.

Basically what I'm trying to figure out is why Martin-Lof definition
is a good definition for randomness of
infinite sequences.

It isn't. At best it is an attempt to quantify the apparent randomness of
the bit stream, this is radically different from the actual randomness of
the bit stream.

There simply cannot exist a test of actual randomness/entropy of a bit
stream. For apparent randomness/apparent entropy there are an infinite
number of them.