What does this notation about ranges mean?

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This might be a very basic question but I ran into this notation in a numerical methods book

Let $$g ∈ C[a, b]$$ be such that $$g(x) ∈ [a, b], \forall x \in [a, b]$$

What does the $$C[a, b]$$ mean?

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The set of all the continuous functions in the interval $[,]$.