# Interpretation of for loop.

for every j != i in {0,....,n-1}

How to interpret this for loop? I never seen this type of definition of for loop.

Is it like - j=0 to n-1; j !=i ; ++j

• It's pseudocode, isn't it? I suppose just take it literally then? Jul 30, 2018 at 3:52
• If i is not defined before the meaning is clearly $for\;(i,j)\;\in\{(a,b) \mid a \in \{0..n-1\} \land b \in \{0,..n-1\} \land a\neq b\}$. Jul 30, 2018 at 12:48

Here is the probable interpretation:

for every $j \neq i$ in $\{0,\ldots,n-1\}$:

code

should be interpreted as:

for every $j$ in $\{0,\ldots,n-1\}$:

if $j \neq i$:

code

This is similar to the way this kind of statement is interpreted in mathematical text.

It is also possible that the roles of $i$ and $j$ should be switched — this should be clear from context, and it's an ambiguity that also exists in mathematical texts.

As mentioned in Evil's answer, if neither $i$ nor $j$ has been defined, then the interpretation is probably

for every $i,j$ in $\{0,\ldots,n-1\}$:

if $i \neq j$:

code

• Upvoted, but note that "for every i, j in {0,…,n−1}" isn't 100% formal either. I think Evil's formulation of that possibility (as two nested loops) is clearer. Jul 31, 2018 at 7:00
• Evil's interpretation is a guess - perhaps the loops should be switched? Jul 31, 2018 at 7:02
• Swapping the order of the inner i and outer j loops has no effect on the semantics of the program. (However, one or the other ordering may well take more advantage of cache effects if we're going to use the loop indices as indices into a 2D array. See Row-major and column-major order.) Jul 31, 2018 at 16:41

There is another interpretation, both $i, j$ might be variables, in that case it is double loop:

for every $j$ in $\{0,\ldots,n-1\}$:

for every $i$ in $\{0,\ldots,n-1\}$:

if $j \neq i$:

code

Simply reading it out loud helps only if we know beforehand if $i$ is fixed variable or another counter, so there is context missing.

• An analogous mathematical notation would be $$\sum_{i,j=0\\i\neq j}^{n-1}$$ Jul 31, 2018 at 9:05

Just read it out loud. "For every $j$ that is not equal to $i$, in $\{0, \dots, n-1\}$."

In my opinion, it would be better to have written "For every $j\in\{0, \dots, n-1\}\setminus\{i\}$."

• My guess is that $i$ is a counter, too. Jul 30, 2018 at 13:13