Properties
These sets clearly form the hierarchy
because they are closures over the 's and .
They are strict subsets (Rose 1984; Gakwaya 1997). In other words
because the hyper operation is in but not in .
- includes functions such as x+1, x+2, ...
- provides all addition functions, such as x+y, 4x, ...
- provides all multiplication functions, such as xy, x4
- provides all exponentiation functions, such as xy, 222x, and is exactly the elementary recursive functions.
- provides all tetration functions, and so on.
Read more about this topic: Grzegorczyk Hierarchy
Famous quotes containing the word properties:
“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 (16321704)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (18031882)