MathLiveFormal definition of a limit at infinity
This states precisely what it means for a function or sequence to approach a limit L as the argument goes to infinity: for every tolerance epsilon there is a cutoff n_0 beyond which all values lie within epsilon of L. It is used to prove limits rigorously in analysis and calculus.
\lim_{x \to \infty} f(x) = L \iff \forall \epsilon > 0 \; \exists n_0 \; \forall x > n_0 : |f(x) - L| < \epsilonWhat the symbols mean
| function or sequence whose values f(x) are considered | |
| the limiting value that f approaches | |
| the argument tending to infinity, ranging over values greater than n_0 | |
| a cutoff value that depends on epsilon | |
| an arbitrary positive tolerance (dimensionless) |
About this formula
- FieldMathematics
- TopicLimits and convergence
- LevelUniversity
- Also calledepsilon-N definition of a limit, epsilon-N limit definition, limit of a sequence definition, definition of limit at infinity, epsilon definition of limit, formal limit definition
- SourceWikidata Q177239
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