> Dan said: > > "You are using the word "function" in at least two > different ways. It might confuse students. There are > biological or mechanical functions and computer > software functions -- all involving actions of some > kind, be they actions of electrons, molecules, cells > or larger parts in the physical world -- and there > are mathematical functions that are abstract > relationships between two or more sets of objects. > (And others, I'm sure.)" > > That's right - and from there one can go on and muse > about how and why the math meaning of the word > "function" has become so abstract and inert.
For most students, a "black-box-input-output" model of functions will suffice. I am, however, focusing more on students tending to proof-based mathematics in their immediate futures. It would be nice if everyone could master these "abstractions" and the basic methods of proof, but few are motivated to do so. I hope my little video and my software will help a bit in this regard.