"The square root of two" is a way to describe a formula. The formula is a construction that generates outputs. The outputs differ depending on how many iterations you run.
There is no "converging" on a quantity. The outputs just gain decimals.
Post by twetch#1832
Perspective A: "The sqrt(2) is a quantity whose value we don't know, can never know, and can only approximate"
Perspective B: "The sqrt(2) is a formula that generates outputs of increasing decimal length, starting with 1.41 and never repeating"
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If I draw the diagonal of a square, do you think that this line has no distance, or that the distance along the line is not a quantity, or something like that? Incommesurate ratios were studied by Euclid.
Euclid could show that his GCD algorithm would not always halt for any two lines that he could draw. But we still have a concrete representation of the irrational quantity in the diagonal of a square. https://en.wikipedia.org/wiki/Euclidean_algorithm
en.wikipedia.org Euclidean algorithm - Wikipedia Actually draw a diagonal on a square, and you will see that, in fact, the diagonal is composed of a finite, countable number of points.
Euclidean geometry mistakenly assumes that space is continuous. With discrete space, there is no incommensurability.