Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: 2 pi i = 0



I think Joel and Bernard are on the same page as I am. To speak the
math that my son and daughter speak, my definition of a function is the
same as their definition of a relation.

Today, if I understand it correctly, all functions are relations, but
not all relations are functions. Today, a relation is any set of
ordered pairs, and a function is a relation with 1-to-1 mapping.

If we have y = 2x + 5 then y has a relation to x and y is also a
function of x.

If we have y = sqrt(x^2+25) then y has a relation to x, but y is not a
function of x. The graph of y versus x is a circle centered on the
origin with radius = 5. It does not pass the 1-to-1 test, or stated
another way the graph does not pass the "vertical line test."

In my school days y = sqrt(x^2 + 25) was every bit as much a function as
y = 2x + 5. The former was a double-valued function except single
valued at x = +or- 5. The latter was a single-valued function. We did
use the "vertical line test" but only to determine if the function was
multi-valued or not.

Bottom line, it appears to me the old-timer definition of function is
the same as the current definition of a relation.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.