How many real numbers exist? New proof moves closer to an answer

Re:How many real numbers exist? New proof moves closer to an... by a1369209993 on Monday July 19, 2021 @03:11AM (#27880016)

> if the axioms at the start are all true.

Axioms are true by definition; that's what "axiom" means. (They might also be false, but (if and) only if your system is inconsistent.)

> Case (1) that machine doesn't really halt

This is not a state of affairs: all you know at any given time is that the machine hasn't halted yet (after some specific finite number of steps), or that it has aquired some termination-precluding invariant like a infinite loop (which you can detect only strictly less than all of).

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Re:How many real numbers exist? New proof moves closer to an... by rssoconnor on Tuesday July 20, 2021 @01:11PM (#27896418)

Axioms are most certainly not true by definition.

Regardless, the particular technical definition of truth I'm using is Tarski's definition of truth[1]. We don't have to agree whether Tarski's definition is "correct", and I'm happy to qualify my use of the word "truth" here, but I'm referring to a specific technical definition here.

[1] https://en.wikipedia.org/wiki/Semantic_theory_of_truth#Tarsk...

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