abstractmath.org GLOSSARY
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
value
¨ The object that is the result of evaluating a function at an element x of its domain is called the value, output or result of the function at x. This meaning is discussed here.
¨ The word value is also used to refer to the object denoted by a literal expression. Most commonly the word is used when the value is a number.
Example
“The value of the expression at 3 is 11.
The values of this expression are always positive.”
Of course, this can be interpreted as “value” in the
previous sense of the function defined by .
Don’t misread “value” as meaning “worth”.
vanish
A function
f vanishes at an input a if f(a) = 0.
variable
vector
The word vector has (at least) three different useful mental representations:
¨ An n-tuple.
¨ A quantity with
length and direction.
¨ An element of a vector space.
Of course, the third representation includes the other two, but with
some subtleties. For example, to think of an element of an abstract n-dimensional vector space as a n-tuple requires choosing a basis for
the space. There is in general no canonical choice of basis.
In computer engineering, the word vector is often used to refer to an n-tuple of any sort of thing, not necessarily
elements of a field (or numbers at all), so that the n-tuple may indeed not be a member of a vector space. I have heard
this usage in conversation but could not find an unequivocal citation for it
for the Handbook.