# Relational Operator - Equi-joins

An Equi-join is a join where the condition (predicate) is an equality.

All other join operations with a predicate other than equality are called theta join

## Syntax

An equi-join links two relations (tables, …) on common values in a column in relation 1 with a column in relation 2.

### Conditional

The restriction conforms to the following syntax when the condition is specified:

• Relational Syntax

$$\LARGE R \bowtie_{R.A = S.A} S$$

• SQL
Table1.column_a = Table2.column_a


### Natural

A natural join is a shorthand equi-join where the equality applied to all shared attributes.

$$\LARGE R \bowtie_{attrs(R) \cap attrs(S)} S$$ where:

• $attrs(R) \cap attrs(S)$ is the intersection of the attributes of R and S.

## Rule

$$\LARGE R_1 \bowtie_{ a = b } R_2 = \sigma_{a=b} ( R_1 \times R_2 )$$

The join of R1 and R2 on A=B is the same that the selection of the cross product of R1 and R2 where A=B.

## Notation

### Sql Notation

#### Equality Notation

select *
from R1 JOIN R2
on R1.A = R2.A


#### Cross product notation

select *
from R1, R2
where
R1.A = R2.A