Similar Properties of e and The Function ez
The function ez is not in C(z) (i.e., is not the quotient of two polynomials with complex coefficients).
For n distinct complex numbers {a1,..., an}, the set {ea1z,..., eanz} is linearly independent over C(z).
The function ez is transcendental over C(z).
Read more about this topic: Exponential Function
Famous quotes containing the words similar, properties and/or function:
“We do not need to minimize the poverty of the ghetto or the suffering inflicted by whites on blacks in order to see that the increasingly dangerous and unpredictable conditions of middle- class life have given rise to similar strategies for survival. Indeed the attraction of black culture for disaffected whites suggests that black culture now speaks to a general condition.”
—Christopher Lasch (b. 1932)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“The intension of a proposition comprises whatever the proposition entails: and it includes nothing else.... The connotation or intension of a function comprises all that attribution of this predicate to anything entails as also predicable to that thing.”
—Clarence Lewis (1883–1964)