Notation $\Delta_a$ to show absolute error I have numerical methods course and studying the subject "errors". Our teacher showed Absolute Error with the notation $\Delta_a$(where $a$ is subscript). For example he wrote $\Delta_a=|a-a_0|$ and later wrote the error of functions like $\Delta_{\sin x}$ or $\Delta_{\cos x}$.
But after I studied some books I saw they write for example $\Delta a$(Where $a $ is not a subscript) and I think it is the correct notation. Am I right about that? If so, then should I use the same notation (with subscript) in the homework problems or exams?
 A: Notation is to ease the communication of mathematics to other people. Thus there is no absolute "right" and "wrong" notation as long as its clear to the reader what you mean by it. If you are writing an article or in a forum like this then you should strive to use the notation that is most commonly used.
In a course - where the homework is you communicating with your lecturer - then its a good idea to use the same notation as used in the lectures or in you textbook. This will make it easier for that person to understand you. If you want to use a different notation then make sure you clearly define it.
For this particular notation if you wrote $\Delta_a$ without defining it then I don't think I would have understood it right away so I would agree that $\Delta a$ is probably more understandable. But then again if by $\Delta a$ you also mean $|a-a_0|$ then this could also be confusing. $\Delta a$ is very often used to denote just $a-a_0$ (no absolute value), e.g. in the definition of the derivative which is sometimes written as $\lim_{\Delta x\to 0}\frac{\Delta y}{\Delta x}$. This might be the reason for using this notation with a subscript - to separate these two meanings.
