Zero to the zero power

Zero to the zero power is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Some programming languages are not exactly consistent (with other programming languages) when raising zero to the zeroth power: $0^{0}$.

Task requirements

Show the results of raising zero to the zeroth power.

If your computer language objects to 0**0 at compile time, you may also try something like: <lang rexx>x = 0 y = 0 z = x**y ··· show the result ···</lang> Of course, use any symbols or notation that is supported in your computer language for exponentiation.

See also

• The Wiki entry: Zero to the power of zero.
• The Wiki entry: History of differing points of view.
• The MathWorld™ entry: exponent laws.
  • Also, in the above MathWorld™ entry, see formula (9): $x^{0}=1$.
• The OEIS entry: The special case of zero to the zeroth power

C

This example uses the standard pow function in the math library. 0^0 is given as 1. <lang C>/*Abhishek Ghosh, 18th March 2014, Rotterdam*/

1. include<stdio.h>
2. include<math.h>

int main() { printf("0 ^ 0 = %f",pow(0,0)); return 0; } </lang>

Output:

0 ^ 0 = 1.000000

D

<lang d>void main() {

   import std.stdio, std.math, std.bigint, std.complex;

   writeln("Int:     ", 0 ^^ 0);
   writeln("Ulong:   ", 0UL ^^ 0UL);
   writeln("Float:   ", 0.0f ^^ 0.0f);
   writeln("Double:  ", 0.0 ^^ 0.0);
   writeln("Real:    ", 0.0L ^^ 0.0L);
   writeln("pow:     ", pow(0, 0));
   writeln("BigInt:  ", 0.BigInt ^^ 0);
   writeln("Complex: ", complex(0.0, 0.0) ^^ 0);

}</lang>

Output:

Int:     1
Ulong:   1
Float:   1
Double:  1
Real:    1
pow:     1
BigInt:  1
Complex: 1+0i

Go

Go does not have an exponentiation operator but has functions in the standard library for three types, float64, complex128, and big.Int. The functions for float64 and big.Int are documented to return 1. The function for complex128 does not have the special case documented. <lang go>package main

import (

   "fmt"
   "math"
   "math/big"
   "math/cmplx"

)

func main() {

   fmt.Println("float64:    ", math.Pow(0, 0))
   var b big.Int
   fmt.Println("big integer:", b.Exp(&b, &b, nil))
   fmt.Println("complex:    ", cmplx.Pow(0, 0))

}</lang>

Output:

float64:     1
big integer: 1
complex:     (0+0i)

Haskell

<lang haskell>import Data.Complex

main = do

 print $ 0 ^ 0
 print $ 0.0 ^ 0
 print $ 0 ^^ 0
 print $ 0 ** 0
 print $ (0 :+ 0) ^ 0</lang>

Output:

1
1.0
1.0
1.0
1.0 :+ 0.0

J

<lang j> 0 ^ 0 1</lang>

Java

<lang java>System.out.println(Math.pow(0, 0));</lang>

Output:

1.0

OCaml

In the interpreter:

# 0.0 ** 0.0;;
- : float = 1.
# Complex.pow Complex.zero Complex.zero;;
- : Complex.t = {Complex.re = nan; Complex.im = nan}
# #load "nums.cma";;
# open Num;;
# Int 0 **/ Int 0;;                 
- : Num.num = Int 1

Perl 6

Translation of REXX.

<lang perl 6>say '0 ** 0 (zero to the zeroth power) ───► ', 0**0</lang>

Output:

0 ** 0 (zero to the zeroth power) ───► 1

Python

<lang python>>>> from decimal import Decimal >>> from fractions import Fraction >>> for n in (Decimal(0), Fraction(0, 1), complex(0), float(0), int(0)): try: n1 = n**n except: n1 = '<Raised exception>' try: n2 = pow(n, n) except: n2 = '<Raised exception>' print('%8s: ** -> %r; pow -> %r' % (n.__class__.__name__, n1, n2))

Decimal: ** -> '<Raised exception>'; pow -> '<Raised exception>'

Fraction: ** -> Fraction(1, 1); pow -> Fraction(1, 1)

complex: ** -> (1+0j); pow -> (1+0j)
  float: ** -> 1.0; pow -> 1.0
    int: ** -> 1; pow -> 1

>>> </lang>

REXX

<lang rexx>/*REXX program shows the results of raising zero to the zeroth power.*/ say '0 ** 0 (zero to the zeroth power) ───► ' 0**0</lang>
using PC/REXX
using Personal REXX
using REGINA output

0 ** 0  (zero to the zeroth power) ───►  1

using R4
output

Error 26 : Invalid whole number (SYNTAX)
Information: 0 ** 0 is undefined
Error occurred in statement# 2
Statement source: say '0 ** 0  (zero to the zeroth power) ───► ' 0**0
Statement context: C:\ZERO_TO0.REX, procedure: ZERO_TO0

using ROO
output

Error 26 : Invalid whole number (SYNTAX)
Information: 0 ** 0 is undefined
Error occurred in statement# 2
Statement source: say '0 ** 0  (zero to the zeroth power) ───► ' 0**0
Statement context: C:\ZERO_TO0.REX, procedure: ZERO_TO0

Standard ML

In the interpreter:

- Math.pow (0.0, 0.0);
val it = 1.0 : real

Tcl

Interactively… <lang tcl>% expr 0**0 1 % expr 0.0**0.0 1.0</lang>