Examples
- The set of all prime numbers is arithmetical.
- Every recursively enumerable set is arithmetical.
- Every computable function is arithmetically definable.
- The set encoding the Halting problem is arithmetical.
- Chaitin's constant Ω is an arithmetical real number.
- Tarski's indefinability theorem shows that the set of true formulas of first order arithmetic is not arithmetically definable.
Read more about this topic: Arithmetical Set
Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)