diff --git a/content/optimal-privacy.md b/content/optimal-privacy.md index acdc4552..5736936a 100644 --- a/content/optimal-privacy.md +++ b/content/optimal-privacy.md @@ -47,11 +47,11 @@ $$f(x,y) = \begin{pmatrix}0 & 1 & 0 & 1 & 0 & 1 & \dots \\\ 1 & 0 & 1 & 0 & 1 & Such a function can be partitioned based on a single bit of information e.g. whether $y$ is divisible by 2: -$$f(x,y) = \begin{pmatrix}1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ 0 & 0 & 0 & \dots \\\ \vdots & \vdots & \vdots & \vdots & \ddots \end{pmatrix}$$ +$$f(x,y) = \begin{pmatrix}1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ 0 & 0 & 0 & \dots \\\ \vdots & \vdots & \vdots & \ddots \end{pmatrix}$$ or not: -$$f(x,y) = \begin{pmatrix}0 & 0 & 0 & \dots \\\ 1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ \vdots & \vdots & \vdots & \vdots & \ddots \end{pmatrix}$$ +$$f(x,y) = \begin{pmatrix}0 & 0 & 0 & \dots \\\ 1 & 1 & 1 & \dots\\\ 0 & 0 & 0 & \dots\\\ 1 & 1 & 1 & \dots \\\ \vdots & \vdots & \vdots & \ddots \end{pmatrix}$$ We can partition each matrix again, based on whether $x$ is divisible by 2 or not. Regardless of which of the above partitioned matrices we start with, the resulting matrices are the same: