Definable Real Number
A real number a is first-order definable in the language of set theory, without parameters, if there is a formula φ in the language of set theory, with one free variable, such that a is the unique real number such that φ(a) holds in the standard model of set theory (see Kunen 1980:153).
For the purposes of this article, such reals will be called simply definable numbers. This should not be understood to be standard terminology.
Note that this definition cannot be expressed in the language of set theory itself.
Read more about Definable Real Number: General Facts, Notion Does Not Exhaust "unambiguously Described" Numbers, Other Notions of Definability
Famous quotes containing the words real and/or number:
“Discourage litigation. Persuade your neighbors to compromise whenever you can. Point out to them how the nominal winner is often a real loser—in fees, expenses, and waste of time. As a peacemaker the lawyer has a superior opportunity of being a good man. There will still be business enough.”
—Abraham Lincoln (1809–1865)
“In a number of other cultures, fathers are not relegated to babysitter status, nor is their ability to be primary nurturers so readily dismissed.... We have evidence that in our own society men can rear and nurture their children competently and that men’s methods, although different from those of women, are imaginative and constructive.”
—Kyle D. Pruett (20th century)