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The Kronecker delta is defined as link to wikipedia: $$\delta_{l,m} = \begin{cases} 1 & \text{if }m=l,\\ 0 & \text{if }m\neq l. \end{cases}$$

I would like to denote the case where: $$ = \begin{cases} 0 & \text{if }m=l,\\ 1 & \text{if }m\neq l. \end{cases}$$

How should this be done?

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$1 - \delta_{m,l}$ is common. – Daniel Fischer Oct 2 '13 at 1:13

How about $1 - \delta_{l, m}$?

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Another possibility would be to use the Iverson bracket. For example, the Kronecker delta is $\delta_{l, m} = [l = m]$, while your "opposite case of the Kronecker delta" would just be $[l \neq m]$.

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