Tuple

A tuple is a set of ordered attributes. They are written by listing the elements within parentheses () and separated by commas, such as (john, smith, 1971). Tuple elements are identified via the attribute name. Tuples have the following properties:

• (a₁,a₂, a₃,…,a_n) = (b₁, b₂,b₃,…,b_n ) if and only if a₁= b₁, a₂=b₂, …,a_n= b_n
• A tuple is not a set; the order of attributes matters as well as duplicate members 
  • (a₁, a₂) ≠(a₂, a₁)
  • (a₁, a₁) ≠(a₁)
• A tuple has a finite set of attributes

In the formal relational model, multi-valued attributes as well as composite attributes are not allowed. This is important to reduce data redundancy and increase data consistency. This isn't strictly true in modern relational database systems because of the utilization of complex data types such as JSON and key-value stores.

There is a lot of debate regarding the application of normalization; the rule of thumb is to apply normalization unless there is a good reason not to do so.