limit (Q9869): Difference between revisions

Latest revision as of 12:24, 27 May 2023

value that a function or sequence "approaches" as the input or index approaches some value

Language	Label	Description	Also known as
English	limit	value that a function or sequence "approaches" as the input or index approaches some value

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\lim _{x\to \infty }f(x)=L:\iff \forall \epsilon >0\exists n_{0}\forall n>n_{0}:|f(n)-L|<\epsilon

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Revision as of 12:24, 27 May 2023 Fire (talk \| contribs) Bureaucrats, Interface administrators, Administrators 132,236 edits ‎Created claim: field of work (P131): mathematics (Q140) ← Older edit	Latest revision as of 12:24, 27 May 2023 Fire (talk \| contribs) Bureaucrats, Interface administrators, Administrators 132,236 edits ‎Created claim: defining formula (P333): \lim_{x \to \infty}f(x) = L :\iff \forall \epsilon > 0 \exists n_0 \forall n>n_0 : \|f(n) - L\| < \epsilon
	Property / defining formula
		$\lim _{x\to \infty }f(x)=L:\iff \forall \epsilon >0\exists n_{0}\forall n>n_{0}:\|f(n)-L\|<\epsilon$ `\lim_{x \to \infty}f(x) = L :\iff \forall \epsilon > 0 \exists n_0 \forall n>n_0 : \|f(n) - L\| < \epsilon`
	Property / defining formula: $\lim _{x\to \infty }f(x)=L:\iff \forall \epsilon >0\exists n_{0}\forall n>n_{0}:\|f(n)-L\|<\epsilon$ / rank
		Normal rank