Re: Adics and other Nonsense

With the formalist perspective it becomes
clear why 1 and 0.99... are distinct from each other.

It does? Well, well...live and learn.
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In formalist mathematics, of which the new real number system is one, 1 and 0.99... are simply symbols and their behavior are specified solely by the axioms. Since 1 and 0.99... are distinct symbols they are distinct elements. In fact, they differ by a dark number d* = 1 - 0.99...

E. E. Escultura
.