actual definition of "asymptote" ------------------------
...is: limit of tangent lines
so [cos(e^x)]/x^2 doesn't have an asymptote, even though
it has a limit at infinity...
(that is, it's a 1st order notion, not a 0th order notion,
 like "limit at infinity")

graphs of inverse functions ------------------------------
in order to understand graphs of inverse functions, you really need to
think of it as a parametric curve (x,f(x)), and the inverse function
as (f(y),y)=(x,f^{-1}(x)), so it's under the linear transform
(0 1)
(1 0)
which is reflection through vector (1,1) (think of eigenvectors)

notation for exp/log ------------------------------------
suggestive notation:
 exp_2(x) := 2^x,
 looks a lot like: log_2(x), so it's easier to see how they're
   inverses
 (and use parens!!! it emphasizes that it's a FUNCTION)

increasing/decreasing -----------------------------------
Given f: X -> Y
where X,Y posets (e.g., X=Y=R), we can define:

increasing:
 if x < x', then f(x) < f(x')
decreasing:
 if x < x', then f(x) > f(x')
non-decreasing:
 if x <= x', then f(x) <= f(x')
non-increasing:
 if x <= x', then f(x) >= f(x')

other terms used are:
strictly increasing
strictly decreasing
increasing
decreasing
...which I don't like b/c constant functions are -not- increasing!

The concept of a function being not increasing but not decreasing
either, like x^3 - x, is -linguistically- very hard for students to
deal with: they have a much easier time dealing with dichotomies
(it's either increasing, or decreasing, right?).
*** same problem as open/closed ***

*** the venn diagram (only non-increasing/non-decreasing functions
  are constant, etc.) helps a lot ***

So it's a hard concept to wrap your head around; you really need to
internalize a complex Venn diagram.
However, the words "non-decreasing/non-increasing" don't help a bit,
b/c they "define by negation"
It's exactly the same problem as "non-negative" (meaning positive or zero).
The clearest solution I've found is to use ``semi-positive'' etc.:
positive      >0
semi-positive \geq 0  (aka, "non-negative")
zero          =0
semi-negative \leq 0  (aka, "non-positive")
negative      <0
(likewise "semi-increasing" and so on;
 compare with "semipositive" matrices (aka, postive semi-definite))


It's too easy to start using a word before you understand what it means.