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A counterargument can be used to rebut an objection to a premise, a main contention or a lemma. Synonyms of counterargument may include rebuttal, reply, counterstatement, counterreason, comeback and response. An attempt to rebut an argument may involve generating a counterargument, or finding a counterexample. [1]
The Syracuse function is the function f from the set I of positive odd integers into itself, for which f(k) = k ′ (sequence A075677 in the OEIS). Some properties of the Syracuse function are: For all k ∈ I , f (4 k + 1) = f ( k ) .
Definitions of objection vary in whether an objection is always an argument (or counterargument) or may include other moves such as questioning. [1] An objection to an objection is sometimes known as a rebuttal. [2] An objection can be issued against an argument retroactively from the point of reference of that argument.
Witsenhausen's counterexample shows that it is not always true (for control problems) that a quadratic loss function and a linear equation of evolution of the state variable imply optimal control laws that are linear.
The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arity of the function. A function that takes a single argument as input, such as f ( x ) = x 2 {\displaystyle f(x)=x^{2}} , is called a unary function .
For example, if a counterargument states that renewable energy is too expensive, the writer could counter this by citing the declining costs of solar technology and its long-term savings. [3] Each counterargument can be presented in a separate paragraph or integrated within the main points to show a balanced perspective. Conclusion:
Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...
The simple contour C (black), the zeros of f (blue) and the poles of f (red). Here we have ′ () =. In complex analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.