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# What is 0 to the 0?

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What is 0 to the 0?

Guest May 14, 2015

#5
+78551
+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
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#1
+90968
+5

It is undefined

Melody  May 14, 2015
#2
+78551
+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
+886
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
+90968
+5

What is the difference between undefined and indeterminate Chris ?

Are they interchangable terms?

Melody  May 14, 2015
#5
+78551
+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
#6
+90968
0

ok thanks Chris :)

Melody  May 14, 2015

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