# Symbol for 'When …'

I have never found one listed anywhere: Is there a symbol for a 'when' condition (example below).

$A=B$ when $A$ is even

• Without words:$$2\,|\,A\implies A=B$$this assures us that only if $A\geq2$ is even then $A=B$. By reversing the arrow we'd mean that $A$ is even only if $A=B$ is true, but the latter is not an hypothesis since it's originally stated as the deduction. – TheVal Nov 3 '14 at 20:37
• Why use a symbol when using when is so clear? – lhf Nov 4 '14 at 1:28
• What's wrong with words? A dense pile of notation is very hard to read and, frankly, if you follow @AndreaL.'s suggestion and write $2|L \Rightarrow A=B$, most people will say, "Er, so two divides $A$ implies that $A=B$. Ohhh. $A=B$ when $A$ is even. Why didn't you just write that?" – David Richerby Nov 4 '14 at 1:29
• sure, i was mostly just wondering as often things like 'then' and others have a notation, if there was one for 'when' – CobaltHex Nov 4 '14 at 4:24
• @DavidRicherby Although I myself tend to not overuse notation, I simply shown the most fitting "symbol" for the deduction that's been proposed by the OP. I'm sure that it's easier to understand using words, but I wanted also to show the opposite case. – TheVal Nov 4 '14 at 19:25

This is the same as "If $A$ is even, then $A=B$", or symbolically "$A$ is even $\Rightarrow A=B$". So, if you really wanted to keep the order as you have it, you could write "$A=B \Leftarrow A$ is even", but you run the risk of others not knowing quite what you mean.

• And this would generally be understood in any discipline? (I know implications from CS) – CobaltHex Nov 3 '14 at 20:35
• It will likely be understood by anyone who knows what an implication is, but I would not say that it is standard notation. Best to check with whatever audience you're writing this for whether or not it would be understood. – Santiago Canez Nov 3 '14 at 20:40
• In other words, it is not very often that you hear "$Q$ is implied by $P$" as opposed to "$P$ implies $Q$", although it does happen. – Santiago Canez Nov 3 '14 at 20:42
• Should I use this implication notation as opposed to 'when', assuming my audience understands implications? I personally prefer the shorter versions of notation – CobaltHex Nov 3 '14 at 20:54
• In any kind of formal setting it is usually preferred to write these things out, so "when" wins. That is, you would likely not even see "$\Rightarrow$" in formal writing, but instead "implies" or written as an if-then statement. Again, it depends on your audience. – Santiago Canez Nov 3 '14 at 21:07

It's an implication: ($A$ is even) implies ($A=B$), or

$$(A \mathrm{\ is\ even})\implies(A=B)$$

If you want to keep them in the original order, you can write "$A = B$ if $A$ is even." This is semantically the same as the other answers. Of course, "if" is not a symbol per se, but it might as well be one, and it's a little clearer and more directly logical than "when".

As said, $A=B\Leftarrow A\text{ is even}$, or $A=B\text{ if }A\text{ is even}$ works, but we can do it slightly differently too; "because" also means the same thing as "if" or "when":

$$A=B\quad\because\,A\text{ is even}$$

Personally, I see "$A=B\text{ if }A\text{ is even}$" the most (and yes, I actually see this quite a bit; my professor likes to state theorems with "if"), and I like to explain why I skipped a bunch of steps on my homework by saying "because" (although I usually don't use $\because$ because it looks a lot like $\therefore$, but is much less used)

• Just for completeness, you can flip it around, too: $$A \text{ is even} \therefore A=B.$$ This notation is a little more… dramatic than $\implies$—I think unnecessarily do. – Sean Allred Nov 4 '14 at 3:09