A problem in mathematics is that mathematicians do not always agree on the definitions of things -- even very fundamental concepts [1] [2] -- and so Wikipedia in the interest of neutrality presents all definitions in use. In a given textbook, an author will choose one set of definitions and stick with them, which makes things manageable for the reader. In Wikipedia, the number of alternative interpretations of a sentence grows geometrically with the number of ambiguous terms.

[1] What is a "natural number" (do they start at 0 or 1?)

[2] What is a "function"? Does it carry along a "co-domain"?