5 ms·

Well, computable numbers are countable, so almost all real numbers are non-computable (also they're dense in R). So while your objection is valid, in practice

Well, computable numbers are countable, so almost all real numbers are non-computable (also they're dense in R). So while your objection is valid, in practice any truly randomly selected real number is non-computable.

sykh 8y ago
A computable number can be a normal number. http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf
OskarS 8y ago
I guess I'm saying: such a basic mistake in terminology in the abstract doesn't bode well for the soundness of the paper in general. Being able to properly tell apart the terms "real number" and "non-computable number" is a fairly basic qualification.
- gowld 8y ago
  It's not a "qualification", it's just some using a slightly different set of definitions for convenience. Anyone "qualified" to read the paper understands the meaning.
- davidgay 8y ago
  A quick check on the author leads to https://en.wikipedia.org/wiki/Nicolas_Gisin https://en.wikipedia.org/wiki/Nicolas_Gisin. I think it's going to be rather safe to conclude that this author is well-aware of the difference between the computable and non-computable parts of R.
ajross 8y ago
To nitpick: to say that "in practice" you won't select a rational is understating the case. Being uncountable, the set of irrationals is infinitely larger. The chance of selecting a rational "randomly" is zero as far (heh) as zero has any practical meaning.
zuminator 8y ago
How does one go about truly randomly selecting a real number?
- Analemma_ 8y ago
  This sort of depends on whether you're talking about "randomly selecting a real number" in the real word or in the mathematically abstract world. In the real world, you can't do it, because almost all the real numbers are non-terminating decimals. Or to put it another way, any selection process is a computation, and almost all the real numbers are uncomputable and so can't be found by any computation. To randomly generate a real number in the abstract, I suppose you could do a random walk of infinite steps on the real number line, with each successive step randomly going left or right and shrinking the distance walked. Off the top of my head I'm not sure if that's rigorous, but it sounds like it would work.
- fredch 8y ago
  Very carefully.
- gowld 8y ago
  Simply write its binary expansion, by flipping coins, (heads=1, tails=0), forever.

sykh 8y ago

A computable number can be a normal number. http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf

OskarS 8y ago

I guess I'm saying: such a basic mistake in terminology in the abstract doesn't bode well for the soundness of the paper in general. Being able to properly tell apart the terms "real number" and "non-computable number" is a fairly basic qualification.

gowld 8y ago
It's not a "qualification", it's just some using a slightly different set of definitions for convenience. Anyone "qualified" to read the paper understands the meaning.
davidgay 8y ago
A quick check on the author leads to https://en.wikipedia.org/wiki/Nicolas_Gisin https://en.wikipedia.org/wiki/Nicolas_Gisin. I think it's going to be rather safe to conclude that this author is well-aware of the difference between the computable and non-computable parts of R.

ajross 8y ago

To nitpick: to say that "in practice" you won't select a rational is understating the case. Being uncountable, the set of irrationals is infinitely larger. The chance of selecting a rational "randomly" is zero as far (heh) as zero has any practical meaning.

zuminator 8y ago

How does one go about truly randomly selecting a real number?

Analemma_ 8y ago
This sort of depends on whether you're talking about "randomly selecting a real number" in the real word or in the mathematically abstract world. In the real world, you can't do it, because almost all the real numbers are non-terminating decimals. Or to put it another way, any selection process is a computation, and almost all the real numbers are uncomputable and so can't be found by any computation. To randomly generate a real number in the abstract, I suppose you could do a random walk of infinite steps on the real number line, with each successive step randomly going left or right and shrinking the distance walked. Off the top of my head I'm not sure if that's rigorous, but it sounds like it would work.
fredch 8y ago
Very carefully.
gowld 8y ago
Simply write its binary expansion, by flipping coins, (heads=1, tails=0), forever.