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 and/or function:
“Despite the hundreds of attempts, police terror and the concentration camps have proved to be more or less impossible subjects for the artist; since what happened to them was beyond the imagination, it was therefore also beyond art and all those human values on which art is traditionally based.”
—A. Alvarez (b. 1929)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worryingas a reflex response to demandnever puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. Worrying and Its Discontents, in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)