According to identity theorem A + 0 =
Answers
Answer:
A+0 = A
WHERE 0 IS CALLED ADDITIVE INVERSE OF A
Explanation:
In complex analysis, a branch of mathematics, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a domain D (open and connected subset), if f = g on some {\displaystyle S\subseteq D}{\displaystyle S\subseteq D}, where {\displaystyle S}S has an accumulation point, then f = g on D.
In complex analysis, a branch of mathematics, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a domain D (open and connected subset), if f = g on some {\displaystyle S\subseteq D}{\displaystyle S\subseteq D}, where {\displaystyle S}S has an accumulation point, then f = g on D.Thus a holomorphic function is completely determined by its values on a single open neighborhood in D, or even a countable subset of D (provided this contains a converging sequence). This is not true for real-differentiable functions. In comparison, holomorphy, or complex-differentiability, is a much more rigid notion. Informally, one sometimes summarizes the theorem by saying holomorphic functions are "hard" (as opposed to, say, continuous functions which are "soft").
In complex analysis, a branch of mathematics, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a domain D (open and connected subset), if f = g on some {\displaystyle S\subseteq D}{\displaystyle S\subseteq D}, where {\displaystyle S}S has an accumulation point, then f = g on D.Thus a holomorphic function is completely determined by its values on a single open neighborhood in D, or even a countable subset of D (provided this contains a converging sequence). This is not true for real-differentiable functions. In comparison, holomorphy, or complex-differentiability, is a much more rigid notion. Informally, one sometimes summarizes the theorem by saying holomorphic functions are "hard" (as opposed to, say, continuous functions which are "soft").The underpinning fact from which the theorem is established is the expandability of a holomorphic function into its Taylor series.
In complex analysis, a branch of mathematics, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a domain D (open and connected subset), if f = g on some {\displaystyle S\subseteq D}{\displaystyle S\subseteq D}, where {\displaystyle S}S has an accumulation point, then f = g on D.Thus a holomorphic function is completely determined by its values on a single open neighborhood in D, or even a countable subset of D (provided this contains a converging sequence). This is not true for real-differentiable functions. In comparison, holomorphy, or complex-differentiability, is a much more rigid notion. Informally, one sometimes summarizes the theorem by saying holomorphic functions are "hard" (as opposed to, say, continuous functions which are "soft").The underpinning fact from which the theorem is established is the expandability of a holomorphic function into its Taylor series.The connectedness assumption on the domain D is necessary. For example, if D consists of two disjoint open sets, {\displaystyle f}f can be {\displaystyle 0}{\displaystyle 0} on one open set, and {\displaystyle 1}1 on another, while {\displaystyle g}g is {\displaystyle 0}{\displaystyle 0} on one, and {\displaystyle 2}2 on another.