Re: a circumference is a function?

In article <1191859845.295903.88010@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Eoghan <lucagalbu@xxxxxxxxx> wrote:
hi all.
I was told a function is a relation that for every element of A
associates one and ONLY one element of B. Now, I have studied the
equation for the circumference,

You mean a circle?

but is it a function?

Well, no; it is a circle. Perhaps you mean, is the circle the graph of
a function?

Because for
every x i have 2 y..

Depends entirely on what "equation" you might have, and how you are
trying to understand it as the potential definition of a function; and
how you are trying to understand the picture of a circle as the
"graph" of a function.

A (non-degenerate) circle on the plane is not the graph of a function
in which the y-coordinate is a function of the x-coordinate, because
it fails the "vertical line test", which is presumably what you are
alluding to.

However, it is entirely possible to describe it as the "graph" of a
function in which both the x and y coordinates are functions of some
other variable (say, "t"), and where, instead of plotting all points
of the form (x,f(x)), we plot all values of the function.

For instance, if we define the function f:R --> R^2, given by

f(t) = (cos(t), sin(t))

then if we plot all the values that f takes, we get exactly the circle
x^2 + y^2 = 1.

You'll note, though, that we are really fudging on the meaning of
"graph"; it means one thing in one case, and something else in
another.


Another question: why the tan is said to be a function?

Because it is.

there are
infinite points (x=PI/2+kPI) where I haven't the y (tanPI/2=infinity).

Plz help!

Okay: first, don't use "plz". Take the bother to write complete,
understandable words. This isn't text-messaging.


What makes you think that the definition of a function requires that
it be defined for "every x"?

A function is a rule that assigns to every valid input one, and only
one, output. The key word here is "valid".

A real function of real variable is one in which every valid input is
a real number, and every output is a real number. The key here is that
"every valid input is a real number" is NOT the same thing as "every
real number is a valid input."

The collection of all valid inputs is called the domain of the
function. The tangent function happens to have a domain that is not
ALL of the real numbers, but that does not make it any less of a
function, just like the square root is a perfectly fine real function
of real variable even though it is not defined at any negative number.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

Relevant Pages

  • Finding shortest path into unweighted undirected graph
    ... that way we can say the graph is unweighted and undirected, ... Almost every algorithm I've found on the net is for directed, ... to node A. We say node A is the center of that circle. ... Lets build trees from nodes - each ...
    (comp.games.development.programming.algorithms)
  • Finding shortest path into unweighted undirected graph
    ... that way we can say the graph is unweighted and undirected, ... Almost every algorithm I've found on the net is for directed, ... to node A. We say node A is the center of that circle. ... Lets build trees from nodes - each ...
    (sci.math)
  • Re: need help with homework
    ... Good intuition as a starter. ... base is a circle then we have a circular cylinder. ... If you have a graph of a function, you make a rule as follows: ...
    (sci.math)
  • Re: Data points for line graph.
    ... > I'm working on a graph with 7 lines. ... > in square, filled in circle, etc.) for each line. ... Charts with Picture Markers ...
    (microsoft.public.powerpoint)