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:
“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 (1803–1882)
“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)