what does it mean by "f: U x I -> S"

what does it mean by "f: U x I -> S"? My material says this function predicts rating of a user u for a new item i. But what is "x" there? Anyone please explain the symbols for me..

The material I used: Recommender system handbook - Ricci

"In order to give a formal definition of the item recommendation task, we need to introduce some notation. Thus, the set of users in the system will be denoted by U,and the set of items by I. Moreover, we denote by R the set of ratin开发者_如何转开发gs recorded in the system, and write S the set of possible values for a rating...

Two of the most important problems associated with recommender systems are the best item and top-N recommendation problems. The first problem consists in finding, for a particular user u, the new item i ∈ I \ Iu for which u is most likely to be interested in. When ratings are available, this task is most often defined as a regression or (multi-class) classification problem where the goal is to learn a function f : U ×I →S that predicts the rating f (u, i) of a user u for a new item i..."

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That is the symbol for Cartesian product