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Undefined (mathematics) In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the possibility of assuming different values). [ 1] The term can take on several different meanings depending on the context. For example:
However it is not appropriate to call an expression "indeterminate form" if the expression is made outside the context of determining limits. An example is the expression 0 0 {\displaystyle 0^{0}} . Whether this expression is left undefined, or is defined to equal 1 {\displaystyle 1} , depends on the field of application and may vary between ...
Division by zero. The reciprocal function y = 1 x. As x approaches zero from the right, y tends to positive infinity. As x approaches zero from the left, y tends to negative infinity. In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.
Undefined value. In computing (particularly, in programming ), undefined value is a condition where an expression does not have a correct value, although it is syntactically correct. An undefined value must not be confused with empty string, Boolean "false" or other "empty" (but defined) values. Depending on circumstances, evaluation to an ...
The graph of a degree 1 polynomial (or linear function) f(x) = a0 + a1x, where a1 ≠ 0, is an oblique line with y-intercept a0 and slope a1 . The graph of a degree 2 polynomial. f(x) = a0 + a1x + a2x2, where a2 ≠ 0. is a parabola . The graph of a degree 3 polynomial. f(x) = a0 + a1x + a2x2 + a3x3, where a3 ≠ 0.
Rational function. In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [ 1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...
Expression (mathematics) In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers ( constants ), variables, operations, functions. Other symbols include punctuation signs and brackets (often used for grouping, that is for ...