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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 diagram accompanies Book II, Proposition 5. [ 1 ] A mathematical proof is a deductive argument for a mathematical statement , showing that the stated assumptions logically guarantee the conclusion.
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 ...
The Latin phrase is attested in a 1501 Euclid translation of Giorgio Valla. [5] Its abbreviation q.e.d. is used once in 1598 by Johannes Praetorius , [ 6 ] more in 1643 by Anton Deusing , [ 7 ] extensively in 1655 by Isaac Barrow in the form Q.E.D. , [ 8 ] and subsequently by many post- Renaissance mathematicians and philosophers.
The argument below is a modern version of Cantor's argument that uses power sets (for his original argument, see Cantor's diagonal argument). By presenting a modern argument, it is possible to see which assumptions of axiomatic set theory are used. The first part of the argument proves that N and P(N) have different cardinalities:
An argument is valid if, and only if, it is necessary that, if all its premises are true, its conclusion is true. [38] [41] [42] Alternatively, an argument is valid if, and only if, it is impossible for all the premises to be true while the conclusion is false. [42] [38] Validity is contrasted with soundness. [42]
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", [1] while they are rational according to the broader requirement that they are based on reason and knowledge.
Proof by intimidation (or argumentum verbosum) is a jocular phrase used mainly in mathematics to refer to a specific form of hand-waving whereby one attempts to advance an argument by giving an argument loaded with jargon and obscure results or by marking it as obvious or trivial. [1]