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I am having a pretty simple question regarding the notation of approximative and exact results on the same line.

Let's use linear approximations as an example.

Let's say that we have $f(x)=ln(3x+1)$. Then, $L(x)=3x$ is a linear approximation of $f(x)$ around $x=0$.

If we have a number, let's use $1.003$, we can use $L(x)$ to get an approximative value of $ln(1.003)$, since $ln(1.003)=f(0.001)\approx L(0.001)$.

At this point, if I want to write the result on a single line, what is the symbol I should use between $L(0.001)$ and the numerical value? Does the "=" symbol refer to the beginning of the expression or the last step I wrote?

In other words, which of the following is the correct notation? $$f(0.001)\approx L(0.001)\approx 0.003$$ or $$f(0.001)\approx L(0.001) = 0.003$$

Luxim
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    It only refers to the last step. And since $0.003$ is the exact value of $L$ at $0.001$, writing $L(0.001) = 0.003$ seems appropriate. – Seven Apr 16 '16 at 02:02

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