Another way of stating this, which I think is rather non-obvious to people who have not studied some amount of pure math, is that technical mathematical definitions are almost never helpful absent a substantial amount of additional context, because their purpose is generally to capture and formalize a much more intuitively-understood idea or motivating phenomena. A professor of mine liked to joke that MathWorld was a website devoted to collecting definitions which were as technically correct as possible while also being useful to nobody[1], and I think the quoted wikipedia passage follows in that tradition beautifully.

[1] I don't know if this is still the case, but it certainly was in the late '00s.