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What is 0 to the 0?

Guest May 14, 2015

Best Answer 

 #5
avatar+87294 
+10

Here's my understanding of it, Melody......

 

11 / 0     is "undefined" because we can't multiply anything by 0 in the denominator to return the "11"  in the numerator 

 

But.....consider......

 

0 / 0

 

We could multiply the denominator by anything to return the 0 in the numerator....thus....this is "indeterminate"....we can't determine  exactly what this "thing"  is......

 

It might be "pi"...it might be "10"....it might be "3.45612".......etc.

 

 

  

CPhill  May 14, 2015
 #1
avatar+92775 
+5

It is undefined

Melody  May 14, 2015
 #2
avatar+87294 
+5

To see why Melody's answer is true......consider  the following where  n is non-zero

 

0n /  0n   =

 

0n-n  =

 

00

 

But....what's the problem????  .....Note that......in the fraction above, the denominator 0n  = 0 .....and we can't divide by 0.......

 

[It's actually more appropriate to term this situation,  "indeterminate" ]

 

  

CPhill  May 14, 2015
 #3
avatar+869 
0

But that number n must be strictly greater than 0, because you can't have 0 to a power less than (or equal to) 0.

EinsteinJr  May 14, 2015
 #4
avatar+92775 
+5

What is the difference between undefined and indeterminate Chris ?

Are they interchangable terms?

Melody  May 14, 2015
 #5
avatar+87294 
+10
Best Answer

Here's my understanding of it, Melody......

 

11 / 0     is "undefined" because we can't multiply anything by 0 in the denominator to return the "11"  in the numerator 

 

But.....consider......

 

0 / 0

 

We could multiply the denominator by anything to return the 0 in the numerator....thus....this is "indeterminate"....we can't determine  exactly what this "thing"  is......

 

It might be "pi"...it might be "10"....it might be "3.45612".......etc.

 

 

  

CPhill  May 14, 2015
 #6
avatar+92775 
0

ok thanks Chris :)

Melody  May 14, 2015

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