in reply to zero to the power zero

Interpreted as the limit of x**x as x approaches 0, mathematically, 0**0 can be defined in terms of L'Hôpital's rule, where it does evaluate to 1.

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Re^2: zero to the power zero
by syphilis (Archbishop) on Feb 18, 2007 at 15:59 UTC
    Even perl hints at this: 
    C:\_32\C>perl -e "print 0.5 ** 0.5"
0.707106781186548
C:\_32\C>perl -e "print 0.05 ** 0.05"
0.860891659331735
C:\_32\C>perl -e "print 0.005 ** 0.005"
0.973856237016479
C:\_32\C>perl -e "print 0.0000005 ** 0.0000005"
0.999992745697443
C:\_32\C>perl -e "print 0.00000000005 ** 0.00000000005"
0.99999999881405
C:\_32\C>perl -e "print 0.0000000000001 ** 0.0000000000001"
0.999999999997007
C:\_32\C>perl -e "print 0.0000000000000001 ** 0.0000000000000001"
0.999999999999996

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    When I was at school (which, admittedly, was a long time ago) there was no question about it. Every real number (including 0) raised to the power of 0 was equal to 1.

    Not sure about other numbers, however ... eg does i ** 0 == 1 ?

    Cheers,
    Rob
    Update:According to Math::Complex: 
    C:\_32\C>perl -MMath::Complex -e "$z = cplx(0, 1); print $z ** 0"
1

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