NaN and Infinity

Special numeric values NaN and Infinity in Internet Object

Special numeric values in Internet Object represent mathematical concepts of "Not a Number" and infinite values. These are used to handle edge cases in numerical computations, such as division by zero or invalid mathematical operations. These values follow IEEE 754 standards and provide a way to represent undefined or infinite results within numeric operations.

Syntax

Special numeric values are expressed as literal keywords:

specialValue = nanValue | infinityValue
nanValue = "NaN"
infinityValue = ["+" | "-"] "Inf"

Structural Characters

Symbol	Name	Unicode	Description
NaN	Not a Number	Multiple	Represents invalid numeric result
Inf	Infinity	Multiple	Represents infinite value
-	Minus Sign	U+002D	Indicates negative infinity
+	Plus Sign	U+002B	Optional positive indicator

Valid Forms

NaN                  # Not a Number
Inf                  # Positive infinity
-Inf                 # Negative infinity
+Inf                 # Positive infinity (explicit)

Optional Behaviors

Literal and Alternate Forms

Special values have fixed representations:

NaN                  # ✅ Standard form
Inf                  # ✅ Positive infinity
-Inf                 # ✅ Negative infinity
+Inf                 # ✅ Explicit positive infinity

Mathematical Behavior

Special values follow IEEE 754 semantics:

# NaN comparisons always return false
NaN == NaN           # false
NaN != NaN           # true

# Infinity comparisons
Inf > 100            # true
-Inf < 0             # true

Invalid Forms

nan                  # ❌ Lowercase not allowed
NAN                  # ❌ All caps not allowed
inf                  # ❌ Lowercase not allowed
INF                  # ❌ All caps not allowed
infinity             # ❌ Full word not supported
-NaN                 # ❌ NaN cannot be signed

Preservation of Structure

Internet Object preserves:

• The exact representation of special values

• Negative sign for negative infinity

• Syntactic fidelity (as written, except that an explicit plus sign is not preserved)

However, it does not interpret:

• The mathematical operations that led to these values

• Domain-specific handling of special cases

• Comparison or equality semantics

Such semantics are the responsibility of the schema layer, validators, or application logic.

See Also

• Number - For standard floating-point numbers

• Values