Search results
Results From The WOW.Com Content Network
This fact is often called the algebraic limit theorem. The main condition needed to apply the following rules is that the limits on the right-hand sides of the equations exist (in other words, these limits are finite values including 0).
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
Chasles' theorem (algebraic geometry) Chevalley's structure theorem (algebraic geometry) Faltings's theorem (Diophantine geometry) Fulton–Hansen connectedness theorem (algebraic geometry) Grauert–Riemenschneider vanishing theorem (algebraic geometry) Grothendieck–Hirzebruch–Riemann–Roch theorem (algebraic geometry)
An expression that arises by ways other than applying the algebraic limit theorem may have the same form of an indeterminate form. However it is not appropriate to call an expression "indeterminate form" if the expression is made outside the context of determining limits. An example is the expression .
This is known as the squeeze theorem. [1] [2] ... For example, an analytic function is the limit of its Taylor series, within its radius of convergence.
In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel , who proved it in 1826. [ 1 ]
Category: Theorems in algebra. ... Abel's binomial theorem; Addition theorem; Amitsur–Levitzki theorem; Ax–Grothendieck theorem; B. Bernstein–Kushnirenko theorem;
The existence theorem for limits states that if a category C has equalizers and all products indexed by the classes Ob(J) and Hom(J), then C has all limits of shape J. [1]: §V.2 Thm.1 In this case, the limit of a diagram F : J → C can be constructed as the equalizer of the two morphisms [1]: §V.2 Thm.2