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Re: zero to the power zero

by randyk (Parson)
on Feb 18, 2007 at 15:30 UTC ( #600700=note: print w/replies, xml ) Need Help??


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'H˘pital's rule, where it does evaluate to 1.

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Re^2: zero to the power zero
by syphilis (Bishop) 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
    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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