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Re: 0^0 = 1?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95578] Re: 0^0 = 1?
  • From: dh <dh at metrohm.com>
  • Date: Thu, 22 Jan 2009 06:58:36 -0500 (EST)
  • References: <gl7211$c8r$1@smc.vnet.net>


Hi,

0^0 means the limit if both base and exponent go to zero. But this 

statement alone is insuffucient, because it does neither say with which 

"speed" they go to zero, nor does it give the direction.

If both have the same speed: Limit[x^x,x->0] we get 0

If the base goes much faster to zero: Limit[( 1/Exp[1/x])^(  x), x -> 0] 

we get less than 1: 1/E. Or even faster: Limit[( 1/Exp[1/x^2])^(  x), x 

-> 0] we get 0. Now, if we take the limit from the right side (below 0): 

Limit[( 1/Exp[1/x^2])^(  x), x -> 0, Direction -> 1] we get Infinity.

If we take complex numbers, there are more direction to choose from.

Therefore, it make sense to say that 0^0 is undefined.

However, sometimes it is convenient to set 0^0->1, provided one knows 

what one is doing.

hope this helps, Daniel



ivflam at gmail.com wrote:

> Mathematica says 0^0 = Indeterminate

> Derive says 0^0 = 1

> 

> May I have any opinions?

> 

> Bruno

> 




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