# What does the multiply sign mean in set

A question about set notation. What does the multiply sign here mean?

$$\omega = \times_{i\in N}T_{i}$$

• It’s called a Cartesian product. For two sets $A$ and $B$, $A \times B = \{ (a, b) \mid a \in A, b \in B \}.$ In your case, it’s just an iterated product.
– user71641
May 20, 2015 at 2:18
• $\times_{i\in N}T_{i} = \{(t_1,t_2,t_3,\dots) : t_i \in T_i \}$ Sep 18, 2015 at 14:41

That is occasionally used as an alternative for $\prod$, meaning an indexed Cartesian product.
Whenever you see a usual symbol you know with a subscript telling you that a variable belongs to a set, it means to carry out that operation on everything with that variable as it's index. You have seen this before likely in the form of summation with big sigma notation. In this case, it means to take the Cartesian product (i.e. form ordered tuples by taking one element from each set) over each of the $T_i$'s.