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Relations

The 30 definitions of the relations library, each with its Epsil spelling, its MathJSON name, its signature and its full description.

Each definition is listed under its Epsil spelling (the MathJSON name when it has none), with its signature in the engine's type syntax. The Standard Library page is the one-page index of every category.

Definitions​

Approx​

(any, any*) -> boolean

Approximate-equality relation (approximately equal).

ApproxEqual​

(any, any*) -> boolean

Approximately-equal relation.

ApproxNotEqual​

(any, any*) -> boolean

Approximately-not-equal relation.

congruent​

MathJSON Congruent · (number, number, modulo: number) -> boolean

Indicate that two expressions are congruent modulo a number

Equal​

(any, any) -> boolean

Equality comparison (equal to).

Greater​

(any, any*) -> boolean

Greater-than comparison (strictly greater than).

GreaterEqual​

(any, any*) -> boolean

Greater-than-or-equal comparison (greater than or equal to).

identicallyEqual​

MathJSON IdenticallyEqual · (any, any) -> boolean

Identity comparison (\equiv).

True iff the operands are equal for every value of their free variables.

isSame​

MathJSON IsSame · (any, any) -> boolean

Compare two expressions for structural equality

Less​

(any, any*) -> boolean

Less-than comparison (strictly less than).

LessEqual​

(any, any*) -> boolean

Less-than-or-equal comparison (less than or equal to).

NotApprox​

(any, any*) -> boolean

Negated approximate-equality relation (not approximately equal).

NotApproxEqual​

(any*) -> unknown

Negated approximately-equal relation.

NotApproxNotEqual​

(any, any*) -> boolean

Negated approximately-not-equal relation.

NotEqual​

(any, any) -> boolean

Inequality comparison (not equal to).

NotGreater​

(any, any*) -> boolean

Negated greater-than relation (not greater than).

NotGreaterNotEqual​

(any, any*) -> boolean

Neither greater than nor equal to.

NotLess​

(any, any*) -> boolean

Negated less-than relation (not less than).

NotLessNotEqual​

(any, any*) -> boolean

Neither less than nor equal to.

NotPrecedes​

(any, any*) -> boolean

Negated precedes relation (does not precede).

NotSucceeds​

(any, any*) -> boolean

Negated succeeds relation (does not succeed).

NotTilde​

(any, any*) -> boolean

Negated similarity relation (not similar).

NotTildeEqual​

(any, any*) -> boolean

Negated approximately/asymptotically-equal relation (not approximately equal).

NotTildeFullEqual​

(any, any*) -> boolean

Negated isomorphism/congruence relation (not isomorphic or congruent).

Precedes​

(any, any*) -> boolean

Precedes relation in an ordering (comes before).

Same​

(any, any*) -> boolean

Structural identity comparison (Epsil ===).

True iff every adjacent pair of operands is structurally identical.

Succeeds​

(any, any*) -> boolean

Succeeds relation in an ordering (comes after).

Tilde​

(any, any*) -> boolean

Generic similarity relation (\sim): similar geometric figures, asymptotic equivalence, or "is distributed as". Inert: stays symbolic.

TildeEqual​

(any, any*) -> boolean

Approximately or asymptotically equal

TildeFullEqual​

(any, any*) -> boolean

Indicate isomorphism, congruence and homotopic equivalence