Is this system random or not?

MadViolinist

Hey dcpo:

Ohh. So if the process of generating a random number includes adding 1 to it, it is non deterministic? So there really is no function involved, like the Y = X+1 like my friend was saying?
Also, just curious, what is your definition of randomness?

Thanks again.

dcpo

I am using non-determinism as my definition of randomness. A function is involved in the construction defined in the OP. We are generating a random number, then we are adding one to it. Remember that this is not a real situation that we are describing, it's a vague idea that we are trying to make precise. I am thinking in terms of a process generating a random number, composed with the function defined by f(x)=x+1, because to me this concept is clear, and it appears to capture the essence of the situation in the OP.

Office_Shredder

MadViolinist, imagine instead the following procedure

1) Generate a random number
2) Add one to this number
3) Subtract one from this number

Is the final output a randomly generated number?

MadViolinist

Hey dcpo and Office-Shredder:

Perhaps I am just paranoid about not using functions in this context. I cannot think of a way to avoid using a function and yet still maintaining the randomness of an element of a domain assumed to be random when introducing the bit about adding a 1.

On a side note:
How are we getting the random number in the first place? If there is a way to get that number without using any composition, then it would be easier for me. Unless, what if there is a random number X in some space which we just suppose to be -1 from some other number we never touched upon. Then, we still record the random number X as X, without ever having to deal with the adding or subtracting of one?
I suppose that would relate to the bit Office Shredder mentioned about some random number+1-1 (=random number).

Thanks for sticking around.

dcpo

I'm not really following you here. There's no need to avoid using a function. As I see it the situation being considered is one where a random number is generated, then 1 is added to it. The question is whether this can be called a random process. I am interpreting random as being non-deterministic, and with this definition the whole process of generating a number then adding 1 to it is non-deterministic. The process of adding 1 to a number that is already known remains deterministic, and can reasonably be described as a function, if you find that kind of formalism helpful (I do, maybe you don't). Again, this is not a real situation we are trying to describe, it's an an intuitive idea we are trying to make precise. Alternative definitions of randomness are fine, but it needs to be clear they don't have an internal logic problem, and they need to be motivated for the situation.

MadViolinist

I guess that solves it. Thanks all.