In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit. The concept is due to Augustin-Louis Cauchy, who never gave an (
ε
,
δ
{\displaystyle \varepsilon ,\delta }
) definition of limit in his Cours d'Analyse, but occasionally used
ε
,
δ
{\displaystyle \varepsilon ,\delta }
arguments in proofs. It was first given as a formal definition by Bernard Bolzano in 1817, and the definitive modern statement was ultimately...
In mathematics, and in particular set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They are named after the symbol used to denote them, the Hebrew letter aleph (
ℵ
{\displaystyle \aleph }
) (though in older mathematics books the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up ).
The cardinality of the natural numbers is
ℵ
...
