I'm reading The Elements of Infinitesimal Calculus by David A. Santos, and I stumbled upon this:
45 Definition Let $m$ and $n$ be non-zero natural numbers with $m < n$. We say that $x^n$ dominates $x^m$ as $x \to \pm \infty$ We also say that $x^n$ goes faster to $\pm \infty$ than $x^m$, or that $x^m$ goes slower to $\pm \infty$ than $x^n$. We write this as $x^m = o(x^n)$. In general, if $\frac{f(x)}{g(x)} \to 0$, we write $f(x) = o(g(x))$ as $x \to \pm \infty$ and if $a(x)−b(x) = o(c(x))$, we write $a(x) = b(x) + o(c(x))$. The term $o(c(x))$ is called the error term.
Am I right to think that this paragraph talks about little-o notation? If so, can please someone explain how it is possible to add whatever $o(x)$ is? I also never saw anyone write an equality sign in this situation. I only saw this used with $\in$, as I assumed $o(x)$ to be a set, not a number. Finally, I only met the "error term" in statistics, and I simply can't think of a way that "error term" could apply here.
Can anyone kindly explain what this paragraph says? Is it OK to use this language? Is "error term" and little-o actually the same thing?
I also found this question: little-o and its properties which also puts an equality where I'd expect the $\in$ sign. If the later seems strange to you, then, here's one reference for example: http://mathworld.wolfram.com/Little-ONotation.html