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 first 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. This (pretty common) usage can cause cognitive dissonance, since the function still exists!

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.