Is there a symbol for a number exactly greater than another [closed]

To be clear, the $\epsilon$ that shows up in things like limit proofs doesn't represent a value "just after" 0. Instead, it represents any value greater than 0, no matter how large or small.

In fact, in the standard construction of real numbers, there is no value small enough to be directly next to 0 - it's an important property that there are no gaps, and as a result if you have a real number bigger than zero then you can always find another real number that sits between it and zero.

You can use notation like $a^+$ to mean "in some neighbourhood arbitrarily close to but strictly greater than $a$", but it's usually best to be careful about not saying that something is equal to it. Instead, you could either define an interval $(a, a + \epsilon)$ (where $\epsilon > 0$ is some arbitrary amount) or you can talk in terms of approaching the point in question, e.g. "as $x \rightarrow a^+$" meaning that $x$ approaches $a$ from above.

There are other structures where you can talk about the number "just after 0". The integers is one case - in Peano arithmetic there is a specific function called the successor function that returns the "next" number. The successor to 0 is 1 ($S0 = 1$), the successor to 1 is 2 ($S1 = 2$), and so on.

If you want a structure that contains the real numbers but has successors, then you wind up getting into things like infinitesimals, but the problem is that if you want to introduce them you start to lose other properties of the reals that you might be used to. For example, if you have a value $dx$ that is somehow "just after 0", then what is $\frac{dx}{2}$? It can't be between 0 and $dx$, so either (a) it equals 0, (b) it equals $dx$, (c) it equals something completely different, or (d) it doesn't have a value. And any of these is a problem, because you're going to find that making $2 \times \frac{dx}{2} = \frac{2 \times dx}{2}$ becomes a lot harder than you might expect.

In the theory of posets (a set $P$ with a partial order $\le$), people use the symbol $\lessdot$ for covering: $x\lessdot y$ for $x,y\in P$ when $x<y$ and there are no elements $z\in P$ with $x<z<y$.

For instance, consider the poset with the following Hasse diagram:

$9\lessdot5$ but $11\not\lessdot 3$ since even though $11<3$, we also have $11<6<3$.

Note: In particular, the real numbers $\mathbb R$ make a poset, so it makes sense to think about whether $x\lessdot y$ for $x,y\in\mathbb R$. It turns out that this is not possible; if $x<y$ then there always exists a $z\in\mathbb R$ (such as $\frac{x+y}2$) such that $x<z<y$.