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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.

Examples

No verified examples yet for this function.

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.

Implementation status

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

References

Notes & additional examples

Worked examples

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

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

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

Notes

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