>>12597370>That's also not a string of strokes, hence not a number. does it refer to a number?
>The definition I gave equates numbers to tally marks, so I actually do have access to them.In your system it is impossible to demonstrate facts like "10^100 * 10^100 = 10^200"
>You couldn't give me a yes or no answer. You don't actually know the answer to the question.If you did, you would have collected million dollars by n>What do you make of "the collection of all fields whose universe is (reals)^2 which is isomorphic to the complex numbers and satisfying the Riemann hypothesis"?
by that same logic, you could solve a famous outstanding problem by explaining whether the expression in
>>12597112 refers to a number. Since you are incapable of doing this, the system of numbers is therefore flawed and non-intuitive
>Do you agree that this is a set? If not, why not?It is a set if the Riemann hypothesis is false and it is not a set if the Riemann hypothesis is true. Explanations have already been given
>I think the whole set theory field is mostly nonsense. But according to the standard dogma, there is only a set of field structures on a set because field operations are functions FxF->F and they, together with distinguished identity and zero elements determine the field. So you have a provable proposition in first order logic which translates to "there is a unique X such that X the collection of all fields whose universe is (reals)^2 which is isomorphic to the complex numbers and satisfying the Riemann hypothesis". So that is a set.Depends what you mean by "standard dogma". Insofar as the standard dogma of set theory is ZFC, what you are describing is not a description of a set, because it is not of the form "{x in X : [property of x holds]}" for some set X but rather of the form "{x : [property of x holds]}" with x presumably varying over all mathematical objects. The latter is not a ZFC-valid way of forming sets, the former is (via the axiom of separation)
