5.1 In some ways a tuple does resemble a record and an attribute a field—but these resemblances are only approximate. A relvar shouldn’t be regarded as just a file, but rather as a “file with discipline,” as it were. The discipline in question is one that results in a considerable simplification in the structure of the data as seen by the user, and hence in a corresponding simplification in the operators needed to deal with that data, and indeed in the user interface in general. What is that discipline? Well, it’s that there’s no top to bottom ordering to the records; and no left to right ordering to the fields; and no duplicate records; and no nulls; and no repeating groups; and no pointers; and no anonymous fields (and on and on). Partly as a consequence of these facts, it really is much better to think of a relvar like this: The heading represents some predicate (or some intension), and the body at any given time represents the extension of that predicate at that time.
5.2 Loosely, the specified remark means the UPDATE operation in question “updates the STATUS attribute in tuples for suppliers in London.” But tuples (and, a fortiori, attribute values within tuples) are values and simply can’t be updated, by definition. Here’s a more precise version of the remark:
Let relation s be the current value of relvar S.
Let ls be that restriction of s for which the CITY value is London.
Let ls′ be that relation that’s identical to ls except that the STATUS value in each tuple is ...