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
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“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
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—Alexander Pope (1688–1744)