An ordered series of numbers is a series, and there is no necessary connection between items.

Not only the numbers can be uncorrelated, but also the numbers themselves can be uncertain. This is the so-called "random sequence". For example, you can say that a 1 is a number: it has a 50% probability of being 1 and the other 50% probability of being 0.

The "definition" you gave may be a statement given in the high school mathematics textbook, which describes what needs to be studied in the "sequence" part of high school mathematics. You only need to master the properties of several series mentioned in the textbook, and you don't have to drill into the dead end of mathematical concepts. After all, ideas are prescribed by people.