# Iverson Bracket

Very simple to explain: if $$P$$ is a statement, $$[P]$$ is 1 if $$P$$ is true and 0 if not. So for example

\begin{aligned} \lbrack 1 < 2\rbrack &= 1 \\ \lbrack 1 > 2\rbrack &= 0 \end{aligned}

It’s like using a boolean as an integer in C or Python.

It’s useful to keep yourself organized when you’re writing summations, especially if you’re summing across terms with a weird condition or if you need to exchange two sums. It’s also useful for writing pathological functions concisely.

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