Which notation is correct

Question

This one: \begin{align} V &= 100 + 1 \\ &\cong 100 \\ &\cong 50+50 \end{align}

or

\begin{align} V &= 100 + 1 \\ &\cong 100 \\ &= 50+50 \end{align}

Answer 1

There is no universal convention: Both the notations you described are used. Your reader will understand both, so you can pick the one you are more comfortable with (but be consistent). If you have a multiline relation like $$\begin{align}A &\approx B\\&\approx C\end{align}$$ there are two ways to interpret the second line:

• As an omission: The left hand side is omitted because it's unchanged. $$\left\{\begin{aligned}A &\approx B\\&\approx C\end{aligned}\right\} \overset{\,\,def}{\iff} \left\{\begin{aligned}A &\approx B\\A&\approx C\end{aligned}\right\}$$ Because you align the lines at the relation this makes sense formally (to me), but hides information about the relation between $B$ and $C$ (e.g. is $B \approx C$ or even $B = C$?). Your reader has to figure that out by himself.
• As a continuation: For reasons of presentation you had to add a linebreak, but the second line continuous the first. $$\left\{\begin{aligned}A &\approx B\\&\approx C\end{aligned}\right\} \overset{\,\,def}{\iff} A \approx B \approx C \iff \left\{\begin{aligned}A &\approx B\\B&\approx C\end{aligned}\right\}$$ I personally find that the alignment doesn't make much sense here. On the other hand the relation between $B$ and $C$ is explicit now, which simplifies the reading.