I wonder if this Xamuel guy is a bit off his nut. He invents a word, "pseudo-real," to classify 0.9999... and other such representations. He eventually castigat

I wonder if this Xamuel guy is a bit off his nut. He invents a word, "pseudo-real," to classify 0.9999... and other such representations. He eventually castigates the reasons behind declaring 0.9999...=1, and then asks a profound question: "The real question is not why 0.9999...=1, but rather, what on earth are real numbers in the first place?" It's OK to ask, of course, but he's asking it in a profoundly silly way. For starters, 0.9999... is no less a real number than 0.9999 (i.e. 9999/10000). If we wish to continue on his line of thought, then we should all concede that any scrawling used to represent a quantity - any quantity, real number or no - is a pseudo-quantity. A scrawling is just not the real thing, whether "quantity" is in fact something real or simply the product of human imagination. Hence, "1" is also a pseudo-real, along with "I", "a", "0.9999...", "cos 0", etc. It's anyone's guess if there is such a thing as a unit of anything at all.