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The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle. A mathematical function has one or more arguments in the form of independent variables designated in the definition, which can also contain parameters. The independent variables are mentioned in the list of arguments that the function ...
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 ...
A loosely associated statement is a type of simple non-inferential passage wherein statements about a general subject are juxtaposed but make no inferential claim. [3] As a rhetorical device, loosely associated statements may be intended by the speaker to infer a claim or conclusion, but because they lack a coherent logical structure any such interpretation is subjective as loosely associated ...
An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. [1] The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion.
The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures.
But even arguments that are not deductively valid may still be good arguments because their premises offer non-deductive support to their conclusions. For such cases, the term ampliative or inductive reasoning is used. [63] Deductive arguments are associated with formal logic in contrast to the relation between ampliative arguments and informal ...
A function that takes two arguments. In logic and mathematics, this is often a function that combines two values to produce a third value, such as addition or multiplication in arithmetic. binary relation A relation involving two terms or elements, defining a particular relationship between pairs of objects from two sets (or from one set to ...
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...