Number
Standard 64-bit floating-point numbers in Internet Object
A Number in Internet Object represents a 64-bit double-precision floating-point value conforming to the IEEE 754 standard. Numbers are scalar primitives used to express integers, fractional values, and special numeric constants.
Numbers in Internet Object support various representations including different bases (binary, octal, hexadecimal), scientific notation, and special values like NaN and Infinity.
Syntax
A number can be expressed in multiple forms:
number = ["-" | "+"] (
decimalNumber
| binaryNumber
| octalNumber
| hexNumber
| scientificNumber
) | specialValue
decimalNumber = digit+ ["." digit+]
binaryNumber = "0b" binaryDigit+
octalNumber = "0o" octalDigit+
hexNumber = "0x" hexDigit+
scientificNumber = (digit+ ["." digit+] | "." digit+) ("e" | "E") ["-" | "+"] digit+
specialValue = "NaN" | "Inf" | "-Inf" | "+Inf"
digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
binaryDigit = "0" | "1"
octalDigit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7"
hexDigit = digit | "A" | "B" | "C" | "D" | "E" | "F" | "a" | "b" | "c" | "d" | "e" | "f"Structural Characters
0-9
Digits
Multiple
Standard decimal digits
.
Decimal Point
U+002E
Separates integer and fraction
-
Minus Sign
U+002D
Indicates negative numbers
+
Plus Sign
U+002B
Optional positive indicator
e/E
Exponent
Multiple
Scientific notation exponent
0b
Binary Prefix
Multiple
Binary number indicator
0o
Octal Prefix
Multiple
Octal number indicator
0x
Hex Prefix
Multiple
Hexadecimal number indicator
Valid Forms
Decimal Base Number
Numbers in decimal format can include integers and fractional values, with optional sign prefixes:
# Simple integers
42 # Integer
-17 # Negative integer
+17 # Positive integer (explicit)
# Fractional numbers
3.14159 # Fractional number
-0.5 # Negative fractional
+0.5 # Positive fractional (explicit)
# Zero
0 # Zero
+0 # Positive zero (explicit)
-0 # Negative zero (explicit)A decimal number consists of one or more digits, optionally preceded by a sign (+ or -), and optionally including a decimal point followed by one or more digits.
Alternative Bases
Numbers can be expressed in binary, octal, or hexadecimal notation:
Binary Numbers (Base-2)
Binary representation uses 0b or 0B prefix followed by binary digits (0-1):
0b1010 # Binary 1010 (10 in decimal)
0B1111 # Binary 1111 (15 in decimal)
0b0 # Binary 0
-0b1010 # Negative binary (-10 in decimal)
+0B1100 # Positive binary (12 in decimal)Octal Numbers (Base-8)
Octal representation uses 0o or 0O prefix followed by octal digits (0-7):
0o755 # Octal 755 (493 in decimal)
0O644 # Octal 644 (420 in decimal)
0o0 # Octal 0
-0o755 # Negative octal (-493 in decimal)
+0O377 # Positive octal (255 in decimal)Hexadecimal Numbers (Base-16)
Hexadecimal representation uses 0x or 0X prefix followed by hex digits (0-9, A-F):
0xFF # Hexadecimal FF (255 in decimal)
0x10 # Hexadecimal 10 (16 in decimal)
0XDeadBeef # Mixed case hex (3735928559 in decimal)
-0xFF # Negative hex (-255 in decimal)
+0x10 # Positive hex (16 in decimal)Case Sensitivity
Prefixes: Both lowercase (
0b,0o,0x) and uppercase (0B,0O,0X) are supportedHex digits: Both uppercase (
A-F) and lowercase (a-f) are valid
0xFF # ✅ Lowercase prefix, uppercase digits
0XFF # ✅ Uppercase prefix, uppercase digits
0xff # ✅ Lowercase prefix, lowercase digits
0Xff # ✅ Mixed case (all equivalent)Scientific Notation
Scientific notation expresses numbers using exponential form with e or E:
1.23e4 # 1.23 × 10⁴ = 12300
1.23E4 # Same as above (case insensitive)
1.23e-4 # 1.23 × 10⁻⁴ = 0.000123
-2.5e+3 # -2.5 × 10³ = -2500
5e3 # 5 × 10³ = 5000
.5e2 # 0.5 × 10² = 50
6.022e23 # Avogadro's number
1e-10 # Very small number
-3.14159e0 # -3.14159 × 10⁰ = -3.14159Scientific Notation Components
Mantissa: The significant digits (before
e/E)Exponent marker:
eorE(case insensitive)Exponent: The power of 10 (can be positive, negative, or zero)
# Format: [sign]mantissa[e|E][sign]exponent
1.5e+10 # Explicit positive exponent
1.5e-10 # Negative exponent
1.5e10 # Implicit positive exponentOptional Behaviors
Literal and Alternate Forms
Numbers support multiple equivalent representations:
42 # ✅ Standard decimal
0x2A # ✅ Hexadecimal (equivalent to 42)
0b101010 # ✅ Binary (equivalent to 42)
0o52 # ✅ Octal (equivalent to 42)
4.2e1 # ✅ Scientific notation (equivalent to 42)Invalid Forms
.5 # ❌ Must have leading digit
5. # ❌ Must have trailing digit if decimal point used
0b # ❌ Missing binary digits
0b12 # ❌ Invalid binary digit '2'
0o89 # ❌ Invalid octal digits '8' and '9'
0x # ❌ Missing hex digits
0xGH # ❌ Invalid hex digits 'G' and 'H'
1.2.3 # ❌ Multiple decimal points
0b 1010 # ❌ Space between prefix and digits
0o 755 # ❌ Space between prefix and digits
0x FF # ❌ Space between prefix and digits
1e # ❌ Missing exponent in scientific notation
1e+ # ❌ Missing exponent digits
1.23ee4 # ❌ Multiple exponent markers
1.2.3e4 # ❌ Multiple decimal points in mantissaPreservation of Structure
Internet Object preserves:
The chosen representation form (decimal, binary, octal, hex, scientific)
Whitespace (non-significant in interpretation)
Syntactic fidelity (as written, except that an explicit plus sign is not preserved)
However, it does not interpret:
Mathematical relationships between values
Precision requirements beyond IEEE 754
Domain-specific numeric constraints
Such semantics are the responsibility of the schema layer, validators, or application logic.
See Also
Number Types Overview - Launcher for all number types and formats
BigInt - For arbitrary-precision integers
Decimal - For fixed-precision decimal arithmetic
Special Numeric Values - NaN and Infinity
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