Concepts are sometimes difficult to get across and sometimes it is
necessary to present them in ways that when taken out of context can
mis-represent or possibly be completely untrue. For example, take the
first part of the definition of "operator" from Wikipedia.
Operator
From Wikipedia, the free encyclopedia
Jump to: navigation <http://en.wikipedia.org/wiki/Operator#column-one>,
search <http://en.wikipedia.org/wiki/Operator#searchInput>
This article is about operators in mathematics
<http://en.wikipedia.org/wiki/Mathematics>. For other uses, see
operator (disambiguation)
<http://en.wikipedia.org/wiki/Operator_%28disambiguation%29>.
In mathematics <http://en.wikipedia.org/wiki/Mathematics>, an operator
is a function <http://en.wikipedia.org/wiki/Function_%28mathematics%29>,
usually of a special kind depending on the topic.
. . .
Looking at "function" from Wikipedia it says ". . . In mathematics, a
function relates each of its inputs to exactly one output. . . ."
From MathWorld, "A multivalued function, also known as a
multiple-valued function (Knopp 1996, part 1 p. 103), is a "function"
that assumes two or more distinct values in its range
<http://mathworld.wolfram.com/Range.html> for at least one point in its
domain <http://mathworld.wolfram.com/Domain.html>. While these
"functions" are not functions
<http://mathworld.wolfram.com/Function.html> in the normal sense of
being one-to-one <http://mathworld.wolfram.com/One-to-One.html> or
many-to-one <http://mathworld.wolfram.com/Many-to-One.html>, the usage
is so common that there is no way to dislodge it. When considering
multivalued functions, it is therefore necessary to refer to usual
"functions" as single-valued functions
<http://mathworld.wolfram.com/Single-ValuedFunction.html>. . . ."
Do these definitions conflict or not? How can the term"multi-valued
function" exist if a function can only be single valued? They are both
are trying to present a concept. Is "square root" single-valued? It
depends. In the domain of natural numbers it is. In the domain of
integers it is not.
Gosh! I'm not sure where I'm trying to go with this. But it seems that
this thread is getting hung up on the specifics of definitions rather
than trying to grasp the concepts they are trying to convey.
dly wrote:
I am trying to learn J terms
If J terms can actually be used to describe J technically why not use
them?
There are not enough forums to have special conversations for native
speakers of APL, C++, Java, Excell Spreadsheet users, Dutch, French,
Cantonese, Polish, the 820 listed living languages of Papua New
Guinea, German...
function, operator, relation...
. . .
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