Definition:Limit

Disambiguation

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Limit may refer to:

• Analysis:
  • Limit of Sequence
  • Limit of Mapping:
    • Limit of Mapping between Metric Spaces
    • Limit of Real Function
    • Limit of Complex Function
  • Limit Superior
  • Limit Inferior
  • Limit of Convergence: a deprecated term for the radius of convergence of a real power series

• Measure Theory
  • Limit of Sets

• Category Theory:
  • Limit of Diagram

• Continued Fractions:
  • Limit of Continued Fraction

• Set Theory and Class Theory
  • Limit Ordinal
  • Limit Element under Well-Ordering

Historical Note

It should be noted that neither Newton nor Leibniz had a clear understanding of the concept of a limit, despite their work on inventing the Calculus.

That understanding came later; the modern concept of a limit was pioneered by the work of Carl Friedrich Gauss and Niels Henrik Abel‎.

However, it was not until Augustin Louis Cauchy, in $1821$, that the limit was given a rigorous definition.

Sources

• 1937: Richard Courant: Differential and Integral Calculus: Volume $\text { I }$ (2nd ed.) ... (previous) ... (next): Chapter $\text I$: Introduction