You didn't ask for a definition of "very similar". I'll define by example: In the first explanation above, Bonny and Daisy are very similar
I interpret that to be interchangable but nevertheless distinct in themselves, not just in the label we have used. The values denoted by 0.99999... and 1 are not distinct except in the labels, in the same way that at the moment 'The man occupying the post of the president of the US' and 'Obama' are two distinct labels for the same thing. The goats, on the other hand, are two distinct goats, whatever we choose to call them, even if we choose to confuse everyone by giving them the same name.