5 ms·

Please describe how it is possible to pick such a number. For example, I can readily imagine how to pick a random 32b float, but that it is an entirely problem

Please describe how it is possible to pick such a number. For example, I can readily imagine how to pick a random 32b float, but that it is an entirely problem with a nonzero probability.

Sinergy2 9y ago
*entirely different
georgewsinger 9y ago
Usually in math we assume the axiom of choice :) https://en.wikipedia.org/wiki/Axiom_of_choice https://en.wikipedia.org/wiki/Axiom_of_choice I'm assuming this could somehow lead to such a "random" pick in the technical sense. In terms of implementation, I'm not aware of an algorithm that can randomly pick a real number on an actual computer. Perhaps a mathematician could show how to pick one on some abstract machine with infinite resources, and not constrained by finite bit representations of numbers.
- red75prime 9y ago
  Run a random number generator (0-9) for each decimal position after the dot in parallel. This should do a trick.
- dragonwriter 9y ago
  > In terms of implementation, I'm not aware of an algorithm that can randomly pick a real number on an actual computer An actual (finite in time and space) computer can't even represent arbitrary real numbers, much less randomly choose them.
  - SomeStupidPoint 9y ago
    A Turing machine can't pick random numbers of any kind. Once you accept that you have an entropy source in the physical world, you can easily be injecting random real numbers (from some range) and in fact, usually are, which are then being binned into integers by ADCs.
  - dorgo 9y ago
    What about PI? We can represent it in terms of "we know what we are talking about" and we can distinguish it from other numbers.
    - leni536 9y ago
      You can only have countable number of first or second order logic statements each defining a specific real number.
  - ouid 9y ago
    Those things sound equivalent, but I don't want to be the one to try to prove it.
stiff 9y ago
In probability theory, when dealing with continuous sample spaces / random variables, events with probability 0 still have a chance of occurring, and events with probability 1 stil l have a chance of NOT occurring, see: https://en.wikipedia.org/wiki/Almost_surely https://en.wikipedia.org/wiki/Almost_surely This strange property comes from strange properties of the real numbers (and uncountably infinite sets) that give rise to things like: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox Measure theory deals with resolving this: https://en.wikipedia.org/wiki/Measure_(mathematics) https://en.wikipedia.org/wiki/Measure_(mathematics)
- ouid 9y ago
  What's an anagram for Banach Tarski? Banach Tarski Banach Tarski. Seriously though, you can do math without invoking the axiom of choice. The formulation of probability doesn't strictly depend on it.

Please describe how it is possible to pick such a number. For example, I can readily imagine how to pick a random 32b float, but that it is an entirely problem with a nonzero probability.

Sinergy2 9y ago

*entirely different

georgewsinger 9y ago

Usually in math we assume the axiom of choice :) https://en.wikipedia.org/wiki/Axiom_of_choice https://en.wikipedia.org/wiki/Axiom_of_choice I'm assuming this could somehow lead to such a "random" pick in the technical sense. In terms of implementation, I'm not aware of an algorithm that can randomly pick a real number on an actual computer. Perhaps a mathematician could show how to pick one on some abstract machine with infinite resources, and not constrained by finite bit representations of numbers.

red75prime 9y ago
Run a random number generator (0-9) for each decimal position after the dot in parallel. This should do a trick.
dragonwriter 9y ago
> In terms of implementation, I'm not aware of an algorithm that can randomly pick a real number on an actual computer An actual (finite in time and space) computer can't even represent arbitrary real numbers, much less randomly choose them.
- SomeStupidPoint 9y ago
  A Turing machine can't pick random numbers of any kind. Once you accept that you have an entropy source in the physical world, you can easily be injecting random real numbers (from some range) and in fact, usually are, which are then being binned into integers by ADCs.
- dorgo 9y ago
  What about PI? We can represent it in terms of "we know what we are talking about" and we can distinguish it from other numbers.
  - leni536 9y ago
    You can only have countable number of first or second order logic statements each defining a specific real number.
- ouid 9y ago
  Those things sound equivalent, but I don't want to be the one to try to prove it.

stiff 9y ago

In probability theory, when dealing with continuous sample spaces / random variables, events with probability 0 still have a chance of occurring, and events with probability 1 stil l have a chance of NOT occurring, see: https://en.wikipedia.org/wiki/Almost_surely https://en.wikipedia.org/wiki/Almost_surely This strange property comes from strange properties of the real numbers (and uncountably infinite sets) that give rise to things like: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox Measure theory deals with resolving this: https://en.wikipedia.org/wiki/Measure_(mathematics) https://en.wikipedia.org/wiki/Measure_(mathematics)

ouid 9y ago
What's an anagram for Banach Tarski? Banach Tarski Banach Tarski. Seriously though, you can do math without invoking the axiom of choice. The formulation of probability doesn't strictly depend on it.