# Kronecker delta for inequality

Kronecker delta return 1, or 0 depending on a conditional statement (if $$i = j$$), for example, $$\delta_{i,j} = 1$$ if $$i = j$$, and $$\delta_{i,j} = 0$$ otherwise. I would like to know if there are conventional symbols for similar expressions with conditional statements such as (if $$i \lt j$$) and (if $$i\leq j$$)?

For instance, a conventional symbol for $$X$$ in the following expression: $$X_{i,j} = 0$$ if $$i \lt j$$, and $$X_{i,j} = 1$$ otherwise.

Let's begin by talking about the Iverson bracket $$[p]$$, which for a claim $$p$$ is equal to $$1$$ if $$p$$ is true or $$0$$ if $$p$$ is false. Thus $$\delta_{ij}=[i=j]$$, while your $$X_{ij}$$ is $$[i\ge j]$$. I'm unaware of any other notation you could use (except, say, $$\sum_{k\ge j}\delta_{ik}$$ or $$\sum_{k\le i}\delta_{jk}$$).