Inequality

Wolfram's chained-comparison form -- v1 rel1 v2, v2 rel2 v3, ... all at once, letting the relation change partway through the chain (0 <= x < 5).

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageInequality✓↗

Inequality(v1, rel1, v2, rel2, v3, ...)the conjunction of every consecutive link, where each relᵢ is one of Equal, NotEqual, Less, LessEqual, Greater, GreaterEqual.

Typed signatures

Type	Package	Applies
(expression, expression, expression, expression*) -> boolean	analytic	always

Domain: Relations

Details

• A chain that uses the SAME relation throughout (0 < x < 5) is already Less or LessEqual etc. taking more than two arguments -- see those heads. Inequality exists for a chain that MIXES relations (0 <= x < 5), which compute-engine's own n-ary comparison heads don't represent.
• Evaluates as the And of its pairwise links, applied through the relation heads compute-engine already ships -- so a fully numeric chain folds all the way to True/False, and a symbolic one is left as And of whatever didn't fold.
• Round-trips with Wolfram, which prints exactly this shape whenever Reduce, FunctionDomain, or a mixed-relation input (0 <= x < 5) produces one -- see packages/wolfram/src/to-wolfram.ts.
• Declines (leaves the call unevaluated) on a malformed chain -- an even argument count, or something other than one of the six relations in a relation slot.

Examples

Basic #

A numeric chain that holds -- 0 <= 2 and 2 < 5

live ↗

In$\mathrm{Inequality}(0, \mathrm{LessEqual}, 2, \mathrm{Less}, 5)$Out$\mathrm{True}$

A numeric chain that fails -- 0 <= 5 but not 5 < 5

live ↗

In$\mathrm{Inequality}(0, \mathrm{LessEqual}, 5, \mathrm{Less}, 5)$Out$\mathrm{False}$

A symbolic mixed chain simplifies to the And of its links

live ↗

In$\mathrm{Inequality}(0, \mathrm{LessEqual}, x, \mathrm{Less}, 5)$Out$0≤x∧x\lt5$

Scope #

A three-link chain -- 1 < 2, 2 <= 2, and 2 < 10

live ↗

In$\mathrm{Inequality}(1, \mathrm{Less}, 2, \mathrm{LessEqual}, 2, \mathrm{Less}, 10)$Out$\mathrm{True}$

Equal and NotEqual are valid links too

live ↗

In$\mathrm{Inequality}(0, \mathrm{Less}, x, \mathrm{NotEqual}, 3)$Out$0\lt x∧x≠3$

A homogeneous chain (same relation throughout) still goes through And here -- write it as Less(0, x, 5) directly for the native n-ary form

live ↗

In$\mathrm{Inequality}(0, \mathrm{Less}, x, \mathrm{Less}, 5)$Out$0\lt x∧x\lt5$

Possible issues #

Declines when a link isn't one of the six relations, rather than guess

live ↗

In$\mathrm{Inequality}(0, \mathrm{Add}, 5)$Out$\mathrm{Inequality}(0, \mathrm{Add}, 5)$

About

Examples	7
Checked against	Wolfram Language 7 agree
Crosswalk	Wolfram Language

See also: Less, LessEqual, FunctionDomain