IsIntervalMember

Tests whether x falls within the interval, honoring Open bounds.

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

IsIntervalMember(Interval(lo, hi), x)True if lo (or) x (or) hi, closed by default, open where wrapped in Open(...)

Typed signatures

Type	Package	Applies
(any, any) -> boolean	combinatorics	always

Domain: Collections

Details

• Open(...) on either bound makes that side strict: IsIntervalMember(Interval(Open(1), 5), 1) is False.
• Only a single Interval(lo, hi) -- Wolfram's union-of-intervals form Interval({a, b}, {c, d}, ...) isn't handled.
• Bounds and x are compared as doubles (via N()) -- exact enough for membership, which only ever needs a comparison.
• An Open(...) bound has no Wolfram transpilation: Wolfram's own Interval object is always closed (Interval[{min, max}] means min <= x <= max, with no open-bound notation at all), so an Open(...) example here stays untranslated rather than round-tripping to a Wolfram call that would silently test the wrong (closed) condition.

Examples

Basic #

live ↗

In$\mathrm{IsIntervalMember}(\mathrm{Interval}(1, 5), 3)$Out$\mathrm{True}$

An exact constant is tested against the endpoints: $2 \le \pi \le 5$

live ↗

In$\mathrm{IsIntervalMember}(\mathrm{Interval}(2, 5), π)$Out$\mathrm{True}$

Scope #

live ↗

In$\mathrm{IsIntervalMember}(\mathrm{Interval}(1, 5), 5)$Out$\mathrm{True}$

live ↗

In$\mathrm{IsIntervalMember}((1, 5\rbrack, 1)$Out$\mathrm{False}$

live ↗

In$\mathrm{IsIntervalMember}(\mathrm{Interval}(1, 5), 6)$Out$\mathrm{False}$

About

Examples	5
Checked against	Wolfram Language 4 agree
Crosswalk	Wolfram Language

See also: IsTrue