# Set notation for ACL matrix

This might not be a computer science specific question and apologies if that is the case but it does come from material related to working out access control lists and I cannot understand the notation and I wonder if someone could break it down for me?

$$A’[s_i,o_j]=A[s_i,o_j] \; ∀(s_i,o_j)≄(s,o)$$

I understand that $$A’[s_i,o_j]$$ is the new resulting matrix after some operation and I think $$s_i$$ and $$o_j$$ are the matrix pairs that are not being amended although I do not know exactly that this is the case or how adding the $$i$$ and $$j$$ denotes this.

This might be way off the mark but is it saying that the new matrix is equal to the old matrix where none of the pairs are equal to the pair being deleted?

I am also looking at a list of set symbols and I cannot find this $$≄$$ listed.

• Presumably it should be $≠$ rather than $≄$, that is, "not equal to". – Yuval Filmus May 18 at 20:21
• Could you break down the statement for me, or confirm that what I think is the right way to interpret it? So the new matrix is equal to the old matrix where for every pair in the old set it is not equal to the pair that were removed? – pac234 May 18 at 20:24
• I don't see any sets there. There is a two-dimensional array $A$. You update it in a way which only changes the $(s,o)$ entry. Perhaps the array represents a set in the following way: $A[s',o'] = 1$ if the set contains $(s',o')$, and $A[s',o'] = 0$ if the set doesn't contain $(s',o')$. – Yuval Filmus May 18 at 20:25
• The notation "$\forall$" stands for "for all". – Yuval Filmus May 18 at 20:27
• Ok this is my fault, I am mixing up set and matrix. A is a matrix and not a set, but it is made up of combinations from a set S and a set O. – pac234 May 18 at 20:29

For any $$(s_i,o_j) \neq (s,o)$$, $$A'[s_i,o_j] = A[s_i,o_j]$$.
The correct symbol seems to be $$\neq$$, "not equal", rather than what you wrote.
The symbol $$\forall$$ means "for all".
The notation $$s_i$$ just means "element number $$i$$ in the set of rows", and $$o_j$$ is similarly "element number $$j$$ in the set of columns". You could just as well have replaced $$s_i,o_j$$ with any two other symbols (other than $$s,o$$).