Assertion: real number | /r/HasProperty | denoted c
Facets:
Source sentences:
text: The set of all real numbers is uncountable; that is: while both the set of all natural numbers and the set of all real numbers are infinite sets, there can be no one-to-one function from the real numbers to the natural numbers: the cardinality of the set of all real numbers (denoted c {\displaystyle {\mathfrak {c}}} and called cardinality of the continuum) is strictly greater than the cardinality of the set of all natural numbers (denoted ℵ 0 {
text: An alternative synthetic axiomatization of the real numbers and their arithmetic was given by Alfred Tarski, consisting of only the 8 axioms shown below and a mere four primitive notions: a set called the real numbers, denoted R, a binary relation over R called order, denoted by infix <, a binary operation over R called addition, denoted by infix +, and the constant 1.