Look at the expression example from the linear algebra ($A: V \to W$ is a linear mapping): $$\operatorname{im} A = \operatorname{range} A = A(V) = \{ A(x) \: | \: x \in V \}$$

Here is a feature: the first three terms $(\:\operatorname{im} A, \operatorname{range} A, A(V)\:)$ are synonyms and usually we choose only one of them to denote the set $\{ A(x) \: | \: x \in V \}$.

Is there a standard recommended notation instead of ordinary "equal to" sign ($=$) to highlight this feature between the terms?

I thought about using "equal by definition" notation $(\operatorname{im} A \triangleq \operatorname{range} A \triangleq A(V) = \{ A(x) \: | \: x \in V \})$ but obviously we can also use it instead the last "equal to" notation in the expression $(\operatorname{im} A \triangleq \operatorname{range} A \triangleq A(V) \triangleq \{ A(x) \: | \: x \in V \})$ and consequently it doesn't higlight the feature described above.


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