Values of The Gimel Function
The gimel function has the property for all infinite cardinals κ by König's theorem.
For regular cardinals, and Easton's theorem says we don't know much about the values of this function. For singular, upper bounds for can be found from Shelah's PCF theory.
Read more about this topic: Gimel Function
Famous quotes containing the words values of, values and/or function:
“The traveller who has gone to Italy to study the tactile values of Giotto, or the corruption of the Papacy, may return remembering nothing but the blue sky and the men and women who live under it.”
—E.M. (Edward Morgan)
“We must be physicists in order ... to be creative since so far codes of values and ideals have been constructed in ignorance of physics or even in contradiction to physics.”
—Friedrich Nietzsche (1844–1900)
“The art of living is to function in society without doing violence to one’s own needs or to the needs of others. The art of mothering is to teach the art of living to children.”
—Elaine Heffner (20th century)