# Two questions regarding mathematical writing

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

• For your statement 1, this would be acceptable, in English, for lectures or work on a board. In written English, people are encouraged to use fewer symbols; for example, the $\Leftrightarrow$ might be avoided. The first statement might be written as "$x^2=4$ is equivalent to $x\in\{-2,2\}$." – Michael Burr Jul 17 '15 at 11:02
• The style of your second statement is common in English mathematics. – Michael Burr Jul 17 '15 at 11:03
• There is an \iff command in LaTeX, it means "if and only if" (which is equivalence). So the symbol exists and means the same. – mvw Jul 17 '15 at 11:06
• @mvw: A nicer version is \Leftrightarrow. I never understood why \iff was made so long. – user21820 Jul 17 '15 at 11:13
• @MichaelBurr: You should transfer your comments into an answer. =) – user21820 Jul 17 '15 at 11:14

Your first statement would be acceptable, in English, for lectures or for work on a board. In written English, people are encouraged to use fewer symbols; for example the $\Leftrightarrow$ might be avoided. Someone might write this statement as "$x^2=4$ is equivalent to $x\in\{-2,2\}$."