# Is there a notation for “must be greater than”?

Is there a maths notation for "must be greater than"? I'm trying to say that in order for a given equation to hold true, x "has to be greater than" 5. Thanks, my maths is a bit rusty!

• If you equation is $f(x)=g(x)$, then $(f(x)=g(x))\rightarrow (x>5)$ should be what you want. If you want to say that the equation holds if and only if $x>5$, then you can write $(f(x)=g(x))\leftrightarrow (x>5)$. – Hayden Mar 1 '15 at 16:11
• In short, there is no such notation. Just write, 'In order for (such and such) to be true, it must be the case that $x>5$' or something like that. – John Gowers Mar 1 '15 at 19:59
• Context would be useful. Where did this come up? – Akiva Weinberger Mar 1 '15 at 20:09

Suppose your equation in question is $f(x)=g(x)$. Then we may write $$(f(x)=g(x))\rightarrow (x>5)$$ which can be read as "$f(x)=g(x)$ implies that $x>5$". (You could add a universal quantifier saying "for all $x$ (blah)", but this is implied.)
Here's a little bit more information dealing with this in terms of propositional logic: Here the symbol $\rightarrow$ isn't just some denotation for "implies"; it actually has mathematical meaning. Given two propositions (things that are either true or false) $P$ and $Q$, the proposition $P\rightarrow Q$ is false only when $P$ is true and $Q$ is false, and true otherwise.
So writing $(f(x)=g(x))\rightarrow (x>5)$ means that we're claiming that it is true. As such, if $f(x)=g(x)$ is true, then it is necessarily the case that $x>5$ is also true.
• @user2524828 Exactly, it read "if and only if" or "is equivalent to". Similarly to how $P\rightarrow Q$ is false only when $P$ is true and $Q$ is false, $P\leftrightarrow Q$ is true only when either both $P$ and $Q$ are true or when both are false (i.e. when they have the same truth-value). – Hayden Mar 2 '15 at 1:25