Re: Increasing and decreasing functions - conflicting authors

"Arturo Magidin" <magidin@xxxxxxxxxxxxxxxxx> wrote in message
news:e4cosh$g87$1@xxxxxxxxxxxxxxxxxxxxx
In article <jcGdnSJMrYDhp_TZRVn-iA@xxxxxxxxxxx>,
Colleyville Alan <nospam@xxxxxxxxxx> wrote:
I am starting to read Stewart's Calculus Early Transcendentals (1999 ed.)
for a Calc I class that will begin in a few weeks. In it he talks about
increasing and decreasing functions and shows the intervals using closed
interval notation. In my College Algebra text (Beecher, Penna, &
Bittinger), they emphatically state that you need to use open interval
notation when discussing increasing, decreasing, or constant intervals as
it
is impossible for a point to be increasing and decreasing at the same
time.

Okay. First, it is not the ->point<- that is increasing or
decreasing. It is the function which is decreasing.

Sloppy wording on my part.

Second: there is this thing called "convention". For some authors, for
example, a function f is "increasing" on an interval if and only if
for all x,y in the interval, if x<y then f(x)<f(y); for others, you
only require f(x)<=f(y)

You are bringing up something I had not noticed or thought of previously.

If the x<y part is left out and only the f(x)<=f(y) is present in the
definition, that seems to imply that the function could be called
"increasing" even if you are reading it "backwards", i.e. right-to-left.
IOW, what is typically shown as a decreaing interval in many textbooks could
be called increasing if you examined it from right-to-left rather than from
left-to-right(e.g. y = -x). Is that the point you were making or did I
totally misinterpret your statement?


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