I am a German mathematics student. I have two questions:
First question: When writing several equivalent equations, we usually write this as:
$x^2 = 4$
$\Leftrightarrow x = \pm 2$
I have never seen this in English, i.e. the usage of $\Leftrightarrow$ to indicate equivalence in a sequence of equations. Is it considered bad style? How would you write this?
Second question: In German, we often declare variables within a sentence similar to:
"The output $x$ depends on the time of default $t$ and on the sum $S$ of all payments made prior to $t$."
Is this correct in English? I am not sure whether or not I have seen this before. If not, what would be an alternative formulation?
Thank you very much in advance