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Nov 1, 2022
# DefinitionS , R S, R S , R Set s. Consider the Equation System
Equation System
Definition
Let S , R S, R S , R { f α ∈ R S } α ∈ A \{f{\alpha}\in R^{S}\}{\alpha \in A} { f α ∈ R S } α ∈ A { b α ∈ R } α ∈ A \{b{\alpha} \in R\}{\alpha \in A} { b α ∈ R } α ∈ A
11/7/2022
defined by
f α ( x ) = b α ∀ α ∈ A f_{\alpha}(x)= b_{\alpha} \text{ }\forall \alpha \in A f α ( x ) = b α ∀ α ∈ A {\alpha \in A}a n d and an d {\alpha} \in R}{\alpha \in A}$ for some Index Set A A A {\alpha}\in R^{S}}_{\alpha \in A}$ our Equation System Functions
Equation System Functions
Definition
S , R S, R S , R f α ( x ) = b α ∀ α ∈ A f{\alpha}(x)= b{\alpha} \text{ }\forall \alpha \in A f α ( x ) = b α ∀ α ∈ A { f α ∈ R S } α ∈ A \{f{\alpha}\in R^{S}\}{\alpha \in A} { f α ∈ R S } α ∈ A
11/7/2022
.