Less

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

x \< y or Less[x, y] yields True if x is strictly less than y on numeric inputs, False if strictly greater or equal, otherwise unevaluated. Chained forms (x \< y \< z) become Inequality, decided pairwise. Per IEEE 754, an Indeterminate argument gives False.

Examples (3)

Every input below was run against the current Mathilda build and its output recorded.

Applications (3)

In[1]:= 2 < 3
Out[1]= True

In[2]:= 5 < 5
Out[2]= False

In[3]:= Less[1, 10]
Out[3]= True

Implementation notes

builtin_less delegates to the shared evaluate_inequality(res, -1, -1), which walks adjacent argument pairs and calls compare_numeric on each. compare_numeric returns -1/0/+1 using exact GMP comparison for integer-like operands, exact cross-multiplied long double comparison for rationals, and a 2^-46 relative-tolerance comparison for inexact reals. Less accepts a pair only when the sign is in {-1, -1} (strictly less). If every pair is strictly increasing → True; any pair that compares 0 or +1 → False; any pair that is not numerically comparable → NULL (the whole chain stays unevaluated). This implements the chained semantics of a < b < c. Greater/LessEqual/GreaterEqual are the same function with different accepted sign sets.

Attributes: Protected.

References

See also: LessEqual, Greater, GreaterEqual

• Source: src/comparisons.c
• Specification: docs/spec/builtins/comparisons.md
• Tests: tests/test_comparisons.c
• Tests: tests/test_deriv.c
• Tests: tests/test_mateigen_direct.c
• Tests: tests/test_parse.c

Notes & additional examples

Notes

< is the operator form of Less. A chained form such as a < b < c parses to Inequality and is decided pairwise.