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:
“Let the day perish wherein I was born, and the night in which it was said, There is a man child conceived.”
—Bible: Hebrew Job, 3:3.
A similar imprecation is found in Jeremiah 20:14-15.
“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)
“Morality and its victim, the mother—what a terrible picture! Is there indeed anything more terrible, more criminal, than our glorified sacred function of motherhood?”
—Emma Goldman (1869–1940)