>>12434183>standard definition not in all elementary textbooks I got this construction of R from Euclid's Elements which is the most widely used and read analysis textbook of all time.
>vague & meaninglessThis criticism is vague and meaningless. What is vague about Def 2.1.1, pic related? Even if one says, "I don't know English so I don't know what both directions means and I'm not competent to use keyboard to google it," the meaning that a line is a Hausdorff space for some kind is plain. This pseudo-intellectual copypasta fails to cite anything that's actually problematic. Instead, they rely on an ethos- and pathos-only rhetorical strategy completely devoid of logos. Who can deny that the meaning of Def 2.1.1 is that a line is a Hausdorff space of some kind? The answer is that anyone can deny it, as has this copypasta's author. However, for a rational onlooker, inexpert in mathematics but at least literate and fluent in English, the meaning of Definition 2.1.1 is that a line is a Hausdorff space. It's not vague. A Hausdorff space is a space such that all its points belong to a ball whose points are also in the space. A 1D ball is an interval whose elements lay to the left and right of the point in question. These are the two directions of infinite extent. While someone who does not know math but only knows English might think the definition is vague due to that ignorance, anyone who knows what it means for a space to be "Hausdorff" will know the exact, precise, and fully rigorous specification of the object given in Def 2.1.1. The precise meaning the other articles sans remarks is similarly easily demonstrable. There is nothing of worth in this copypasta aside from a decent, though too pretentious and/or pedantic, imitation of a sincerely scholarly tone.
>fails, to mention, however, What the pseudo-critic does not fail to mention so much as he simply avoids it, is that I prove these numbers do exist in *the* most standard definition of R: Euclid's.
