User:Sphinx-muse/sandbox

If you are not going to reform the way in which mathematics is presented, you will need to do the atrocity of creating a separate major subject section called "mathematics for dummies". As an example, I proposed by editing that the article with the misordered title "bijection, injection, surjection" should begin with the following:

The existence of these three terms proves Plato's assertion in Cratylus that [388e][1] "it is not for every man, Hermogenes," [389a][2] "to give names, but for him who may be called the name-maker; and he, it appears, is the lawgiver, who is of all the artisans among men the rarest." The needed concepts are three: 'one-one', 'onto' and their combination 'one-one and onto'. To read the mathematical literature, we will unfortunately need this bijection: {one-one, onto, one-one and onto} = {injection, surjection, bijection}. See Rosenlicht[3]: (1) "A function [...] is called [...] one-one, if different elements of [the domain] correspond under [the function] to different elements of [the codomain.]", page10. (2) "A function [...] is called onto if each element of [the codomain] corresponds under [the function] to some element of [the domain]", page 10. "If [a function] is both one-one and onto it is called one-one onto", page 10.

[1]   Plato, Cratylus [388e] http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0172%3Atext%3DCrat.%3Asection%3D388e [2]   [Plato, Cratylus 389a] http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0172%3Atext%3DCrat.%3Asection%3D389a [3]   Introduction to Analysis by Maxwell Rosenlicht, Dover (1986) unabridged and unaltered republication of the work first published by Scott, Foresman and Company, 1968.