How do I write this in proper notation?

Question

I was wondering if anyone could help with the below. I don't usually write maths so I'm not even sure what I'm trying to search for.

I want to write the below as a single equation because in reality C and J are quite large terms.

$V_1=C+J_2$ and $V_2=C+J_1$

Something like: For $i=1,2$

$V_i = C+J_{(\text{the other variable})}$

Thanks,

Kat

I suggest to take a photo the original your question and attach it with this question. May Be helpful. — Amin235, Jan 02 '18 at 11:56
A photo of what please? I have edited the question so it might make more sense? — Kat Bailes, Jan 02 '18 at 11:58
In a case this small this should probably just be explicit, but if you really wanted you could do something like $1.5+(-1)^{i+1}/2$. — Ian, Jan 02 '18 at 12:02
There are a number of approaches that could be taken - which one would be appropriate would depend on what you mean by "in reality... quite large terms." — user361424, Jan 02 '18 at 12:03
$V_i=C+J_{3\oplus i}$ for $i=1,2$, where I mean by $\oplus$ the $xor$ between integer numbers. For example, $1+3=01\oplus 11=10=2$. — Amin235, Jan 02 '18 at 12:05

P Vanchinathan · Answer 1 · 2018-01-02T12:46:29.670

I have a problem with your question. I strongly feel you are asking a wrong question.

When we write (mathematics or anything) one thing to keep in mind is whether we are able to communicate clearly and quickly.

Something that occupies less space in print is most likely takes extra time on the part of the reader to unravel. Here one extra equation is a matter of typing 4 or 5 letters. It is not worth the trouble to pack two equations into one.

Someone said at the end of a long letter "Sorry for writing a long letter, I don't have the time to write a short one"!

The answers given to your question (accepted one and other) are at best amusing and not at all easy on the eyes, and puts extra burden on the reader. Writing them as two equations looks best. Look at the comments to the answer seeking clarifications, that should make my point clear.

md2perpe · Accepted Answer · 2018-01-02T12:14:53.280

1

One way: $$V_i = C + J_{3-i}, \quad i=1,2$$

Another: $$\mathbf{V} = \sigma \mathbf{J} + \mathbf{C}, \quad\text{where} \,\mathbf{V} = \left(\begin{matrix}V_1 \\ V_2\end{matrix}\right), \,\mathbf{J} = \left(\begin{matrix}J_1 \\ J_2\end{matrix}\right), \,\sigma = \left(\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right), \,\mathbf{C} = \left(\begin{matrix}C \\ C\end{matrix}\right) $$

edited Jan 02 '18 at 12:14

answered Jan 02 '18 at 12:02

md2perpe

26,770

Thats great thanks! I'll use the top one because its easier in this instance, but the bottom answer might be useful in the future! – Kat Bailes Jan 02 '18 at 12:09
Where is J term in your second expression? – Your IDE Jan 02 '18 at 12:11
@YourIDE. The second $\mathbf{V}$ should be $\mathbf{J}$. I've fixed the formula now. – md2perpe Jan 02 '18 at 12:15

score 0 · Answer 3 · answered Jan 02 '18 at 12:01

0

$$V_i=C+J_{i\%2+1} \quad \forall \quad i=1,2$$ if this is what you're asking for.

answered Jan 02 '18 at 12:01

Your IDE

1,273

I think so, thanks. What does the % in i%2+1 mean? – Kat Bailes Jan 02 '18 at 12:04
$i%2$ gives the remainder when i is divided by $2$ i.e., $i%2=0$ if $i=2$ and $i%2=1$ if $i=1$. So, $i%2+1$ gives the alternate values of $2$ and $1$ respectively( i.e., opposite to that of $i$ in $V_i$ – Your IDE Jan 02 '18 at 12:08

How do I write this in proper notation?

3 Answers3