Search results
Results from the WOW.Com Content Network
In some mathematical contexts, undefined can refer to a primitive notion which is not defined in terms of simpler concepts. [4] For example, in Elements, Euclid defines a point merely as "that of which there is no part", and a line merely as "length without breadth". [5]
Given a line and any point A on it, we may consider A as decomposing this line into two parts. Each such part is called a ray and the point A is called its initial point. It is also known as half-line (sometimes, a half-axis if it plays a distinct role, e.g., as part of a coordinate axis). It is a one-dimensional half-space. The point A is ...
For example, the texts produced by the University of Chicago School Mathematics Project (UCSMP) use a system which, besides some updating of language, differs mainly from the SMSG system in that it includes some transformation concepts under its "Reflection Postulate". [47] There are only three undefined terms: point, line and plane.
Alfred Tarski explained the role of primitive notions as follows: [4]. When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings.
A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .
In poetry, a dropped line is a line which is broken into two lines, but where the second part is indented to the horizontal position it would have had as an unbroken line. For example, in the poem "The Other Side of the River" by Charles Wright , the first and second lines form a dropped line, as do the fourth and fifth lines: [ 1 ]
[3] [4] Likewise, for a function of several real variables, a critical point is a value in its domain where the gradient norm is equal to zero (or undefined). [ 5 ] This sort of definition extends to differentiable maps between R m {\displaystyle \mathbb {R} ^{m}} and R n , {\displaystyle \mathbb {R} ^{n},} a critical point ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 January 2025. Look up undefined in Wiktionary, the free dictionary. Undefined may refer to: Mathematics Undefined (mathematics), with several related meanings Indeterminate form, in calculus Computing Undefined behavior, computer code whose behavior is not specified under certain conditions Undefined ...