Comparison Predicates

Inclusive Comparisons

Inclusive comparisons keep the equality boundary.

highlighted = computed this step

Inclusive comparisons

The inclusive forms keep equal values plus the ordered side.

≤ and ≥\le \text{ and } \ge

Less than or equal

The less-than-or-equal example keeps 3 rows.

le TRUE=3\text{le TRUE}=3

Comparison examples are tiny finite-table transforms with SQL-style TRUE/FALSE/UNKNOWN results; SQL dialect completeness, type coercion, optimizer behavior, indexing, and product claims are out of scope.

Less-than-or-equal comparison: base rowsidnameqtycity1alpha3Austin2beta7Boston3gamma7NULL4delta10Denver5epsilonNULLAustin Comparison result per rowsourceleftValueoprightValuetruthoutputRole03le7TRUEkept17le7TRUEkept27le7TRUEkept310le7FALSEdropped4NULLle7UNKNOWNdropped WHERE-style TRUE-only output rowsidnameqtycity1alpha3Austin2beta7Boston3gamma7NULL Comparison factsfactvalueinputRowCount5trueCount3falseCount1unknownCount1outputRowCount3droppedRowCount2orderedComparisonyeswhereKeepsTRUE_only_source_order

Greater than or equal

The greater-than-or-equal example keeps 3 rows.

ge TRUE=3\text{ge TRUE}=3

Comparison examples are tiny finite-table transforms with SQL-style TRUE/FALSE/UNKNOWN results; SQL dialect completeness, type coercion, optimizer behavior, indexing, and product claims are out of scope.

Greater-than-or-equal comparison: base rowsidnameqtycity1alpha3Austin2beta7Boston3gamma7NULL4delta10Denver5epsilonNULLAustin Comparison result per rowsourceleftValueoprightValuetruthoutputRole03ge7FALSEdropped17ge7TRUEkept27ge7TRUEkept310ge7TRUEkept4NULLge7UNKNOWNdropped WHERE-style TRUE-only output rowsidnameqtycity2beta7Boston3gamma7NULL4delta10Denver Comparison factsfactvalueinputRowCount5trueCount3falseCount1unknownCount1outputRowCount3droppedRowCount2orderedComparisonyeswhereKeepsTRUE_only_source_order

Summary

The equality boundary is included in both comparisons.

boundary included\text{boundary included}