Over the years, I have had many questions I left unanswered regarding notation. Forgive the fact that the points in this list are somewhat unrelated, but I thought it best to group them all in one question:

1. When solving a quadratic equation by factorising, it splits into two equations. For example, $x^2-5x+6=0\implies (x-2)(x-3)=0$. Here, we split the equation into two, to find that $x$ can be either $2$ or $3$. So am I right (notation wise) in concluding $$x=2~~~\veebar~~~x=3$$ where '$\veebar$' denotes an exclusive or. I figured using simply '$\vee$' would make no sense because $x$ couldn't be both at one given time.

2. When performing row operations (in Gaussian Elimination, for example) what symbol do you place between one matrix and another? A lecturer of mine used to use '$\sim$' meaning 'leads to'. For example: $$\left(\begin{array}{ccc|c}1&2&3&3\\3&5&6&5\\7&8&9&9\end{array}\right)$$ $$\sim \left(\begin{array}{ccc|c}1&2&3&3\\0&-1&-3&-4\\7&8&9&9\end{array}\right) \begin{matrix}~\\-3R_1+R2\\~\end{matrix}$$ and what about the operations themselves? Are they written besides the matrix as done above, or above them? Another lecturer of mine used to write $-3R_1+R_2\longrightarrow R_2$ meaning that $-3R_1+R_2$ is placed in the new $R_2$.

3. This one is more about typsetting than actual notation. Half of the books I see write $\displaystyle\frac{dy}{dx}$ and $\displaystyle\int\dots\,dx$; the other half write $\displaystyle\frac{\text{d}y}{\text{d}x}$ and $\displaystyle\int\dots\,\text{d}x$. Should the differential operator be typset upright ($\text{d}$) or italicised ($d$)?

I appreciate any insight you could give me on these matters. Forgive my notational pedantry.

• Wow, that sure is notational pedantry :) For part $1$ you are right- the quadratic is logically equivalent to the exclusive or. However, you could just as easily have put a regular or in there, the exclusiveness would be implicit because of the way the mathematical universe is :) As for the other parts, I will cop out and just say it is a matter of choice ;) – Colm Bhandal Jan 13 '16 at 18:30
• @ColmBhandal Haha, just my mathematical OCD eating away at me. Thanks :) – Luke Collins Jan 13 '16 at 18:31

1. $\lor$ symbol can also be used. It is used in several textbooks without fail. About the symbol you have used, I checked that and found that you can surely use it , it is logical no doubt. Nevertheless, the word "or" can also be used.
2. I would prefer the notation put forward by your second lecturer. And the use of $\sim$ is also correct.
3. Upright $\frac{dy}{dx}$ is preferred.