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The term undefined should be contrasted with the term indeterminate. In the first case, undefined generally indicates that a value or property can have no meaningful definition. In the second case, indeterminate generally indicates that a value or property can have many meaningful definitions.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
The introduction says: "Slope, as a practical term, is not defined for theoretically perfectly horizontal or vertical lines." I have no argument that the slope of a vertical line is undefined, as has been discussed on this page, but a horizontal line? Isn't the slope zero, as I was taught in high school?
The terms themselves are undefined. Hilbert once remarked that instead of points, lines and planes one might just as well talk of tables, chairs and beer mugs. [ 3 ] His point being that the primitive terms are just empty shells, place holders if you will, and have no intrinsic properties.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.
Alfred Tarski explained the role of primitive notions as follows: [2]. 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.
Steve Bannon suggested falsely that President-elect Donald Trump could run for president again in 2028, despite the Constitution’s two-term limit on the office.. The podcaster and former White ...
[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 ...