• Introduction
• Iteration
  • Summation
  • Product
  • Set Notation
  • Nested Iteration
  • Conditions on indices
  • Union and Intersection
  • General Iteration
• General Symbols
  • Cases
  • Function Composition
  • Set Containment
  • Kronecker
• Operations
  • Factorial
  • Binomial
• Differentiation
  • Derivative
  • Partial Derivative
  • Gradient

Set notations $\sum\limits_{x\in S} \operatorname{f}(x)$, $\sum\limits_{i\in I}\operatorname{f}(x_i)$

Here, we will only use the sum $\sum$ symbol, as the index variants are the same for all others.

The set notation is very common when you are not dealing with a neat sequence of increasing numbers.

A set is just a "collection of unique things", so no duplicates. Most programming languages have some kind of set type included. More generally, if you are programming, this usually comes down to having some iterable collection, even just arrays.

You will generally find this notation in two versions:

$\sum\limits_{x\in S} \operatorname{f}(x)$: Go through each element of the set $S$, plug it in some function $\operatorname{f}$ and use the result as a term in the sum

$\sum\limits_{i\in I}\operatorname{f}(x_i)$: Go through each index in the set $I$, plug the $i$-th element in some function $\operatorname{f}$ and use the result as a term in the sum.

Code $\sum\limits_{x\in S} \operatorname{f}(x)$:

Code $\sum\limits_{i\in I}\operatorname{f}(x_i)$: