Consider the different uses below
”A person comes into a bar… ” – which I take to be a description of a joke which can be told without knowing the person’s actual name. This is as contrast to
A story about Obama, which might require the name to be presented.
I now wonder in a similar intuitive way (please take my ignorance into account) what mandate I get from using the axiom of choice.
Does it give me the right only to choose a number without actually knowing the value of the number, as in alternative 1, or does it, as in alternative 2. give me access to an expansion in a base, i.e. an infinite series which is available to me even if it requires an infinite instruction (and cannot be given in a finite form)?
Edit: I take my comment below as my edit to try to comply with the site´s rules for clarity:
@Mosher To rephrase my question to fit your function: Do you know, from the AC, only that such a function exist, or does the AC allow you to choose a particular case of this function - or do you perhaps consider these alternatives to be one and the same?
I see it as saying that a real number exist that you don´t know vs. allowing you to choose a particular number (in the form of a particular form of an infinite set) – or whether this is the same thing in your opinion?