I suggest removing this paragraph (unfortunately this will affect page breaks). I don’t think this paragraph is correct, and the rest of the section doesn’t seem to reference the information contained in this paragraph.

Computer processors implement many functions that are not (implemented in terms of) polynomials over any field, such as saturation arithmetic, operations on n-bit words (eg AND, OR, XOR, number of bits set to 1, bit shifting, etc), various comparisons, bit packing/unpacking, integer/floating point conversions, and many others. See for example here:

https://en.wikipedia.org/wiki/X86_instruction_listings

The information that functions like logarithms are computed in terms of polynomials is also not entirely correct. Taylor series expansion is one of the techniques but even then it is only part of the algorithm. For more details, see:

http://math.stackexchange.com/questions/61209/what-algorithm-is-used-by-computers-to-calculate-logarithms

I plan to inform my electronic collections librarian to tell her Elsevier contacts…

]]>I like the “factorization” language better than the “multifunction” language because it sticks to just talking about “functions”, and it also prepares students for thinking about categorical arguments in the future.

]]>Let pi: A \to B be a surjection. We are attempting to define a function f: B \to C. What we have is a function g: A \to C. Checking that f is “well defined” means that we need to check that if pi(a_1) = pi(a_2) then g(a_1) = g(a_2). In this case, g must factor through pi.

I advocate this viewpoint in this question on MathOverflow:

Can you think of any cases where we need to check that a function is well defined which does not fit into this framework? If not, I think forcing students to find out the “hidden” function pi, and use this “factorization theorem” every time they want to justify that a map is “well defined” might help to clear up some of these issues.

]]>However, I am quite sure they will now continue the negotiations with Elsevier to come to a “better” agreement. The question is, how much better it will be…

]]>Just very recently, DEAL decided not to continue the agreement with Elsevier (German press statement here: https://www.leopoldina.org/fileadmin/redaktion/Publikationen/Allianz/2016_12_02_DEAL.pdf).

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