Question

\[{\large 0^0}=\]

Answer 1

Anything to the power 0 = 1

Answer 2

\[\huge \mathrm{\mathbf{indeterminate}}\]

Answer 3

?

Answer 4

yes indeterminate

Answer 5

Commonly it's taught that 0 to the zero power would be 1.

Answer 6

http://www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml

Answer 7

\[0^0=\frac {0^1}{0^{-1}}\]

Answer 8

ops typo

Answer 9

\[0^0=0^10^{-1}\]

Answer 10

0^0 is indeterminate because:

1) it cannot be determined whether it is 1 or 0 because of conflicting ideas that anything raised to 0 is 1...and 0 raised to anything is 0

2) it came from 0^a/0^a let us assume a is any number except 0... 0/0 would be indeterminate

Answer 11

\(\Large \color{MidnightBlue}{\Rightarrow 0^0 = {0^1 \over 0^1} }\)

UNDEFINED.
Maybe that gets it.

Answer 12

the first reason is the more valid one rather than the second

Answer 13

because the first one is the real reason...the second one i just made up..but does make sense

Answer 14

This is the conflict of two statements.
1) Anything raised to the power 0 is 1.
2) Anything divided by 0 is undefined.

Well, so I guess you can't raise 0 to the zero power. So it is undefined.

Answer 15

conflicting ideas? aren't these ideas ment to be mathematically true, .. and provable.

Answer 16

on a fun note though...who can tell me why \[\huge 1^{\infty} = indeterminate\]

conflicting because 0^0 satisfies both conditions

Answer 17

But lgba,

\(\Large \color{MidnightBlue}{\Rightarrow 1^{n} = 1 }\)

Answer 18

0! = 1
Does that fact lead to\[0^{0}=1\]

Answer 19

exactly...so why is that indeterminate?

Answer 20

Because n is indeterminate.

Answer 21

good point @kropot72

Answer 22

According to some Calculus textbooks, 0^0 is an "indeterminate form." What mathematicians mean by "indeterminate form" is that in some cases we think about it as having one value, and in other cases we think about it as having another.

Source: http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

Answer 23

that refers to the 0^0 may be 1 or 0 so it is indeterminate

Answer 24

\[\frac{0\times0\times0}{0\times0}=\frac{0^3}{0^2}=\]

Answer 25

And anything divided by 0 is undefined. Yes.


\(\Huge \color{MidnightBlue}{INDETERMINATE }\)

Answer 26

I like how we're sharing our ideas.

Answer 27

0^0 = ?; 0^1= ?

2^1 = 2; 2^0= 1
1^1 = 1; 1^0= 1

Answer 28

0^1=0

Answer 29

Check out this article, i thought it was pretty interesting.
http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/

Answer 30

Even in wikipedia http://en.wikipedia.org/wiki/Indeterminate_form#The_form_00

Answer 31

\(\Large \color{MidnightBlue}{\Rightarrow 2^1 = {2^2 \over 2} = 2 \text { and } 2^{0} = {2^1 \over 2} = 1 }\)

Similarly,
\(\Large \color{MidnightBlue}{\Rightarrow 0^1 = 0 \text{ and } 0^{0} = {0^1 \over 0} }\)

But, that'd be undefined.

Answer 32

@ParthKohli, 0/0 is indeterminate. However n/0 = infinity, where n is not equal to zero

Answer 33

TYPE IN YOUR CALCULATOR \[\log 1 \div \log 0\] and see if the answer is 0

Answer 34

MATH ERROR

Answer 35

n/0 is not infinity. the limit as x approaches 0 of n/x is infinity. n/0 is undefined.

Answer 36

Anything over 0 = UNDEFINED

Answer 37

But guys, isn't \(\infty\) = Undefined?

Answer 38

http://www.youtube.com/watch?v=RQSnbJd04GY

Answer 39

that's because there's no such thing as log 0 but if 0^0 = 1 then log_0 1 must be equal to 0...but since it's not...0^0 =/= 1

Answer 40

infinity is a just a term. its not a number.

Answer 41

http://www.youtube.com/watch?v=kEnwac_9lyg

Answer 42

http://www.youtube.com/watch?v=scwICYsRv-o

Answer 43

Neither is undefined. Undefined is also a term.

Answer 44

\[\infty = undefined\] BUT \[undefined \ne \infty\]

Answer 45

SO, if i ever measured 0^0 in a situation,
it would depend on what that situation was as to the values that corresponds to the measurement 0^0

Answer 46

it actually makes more sense than you think

Answer 47

@UnkleRhaukus thmn you use calculus lol

Answer 48

then*

Answer 49

The thing is, we wouldn't ever go through this kind of terms. But, once in a while, it's good to know all about this fancy stuff.

Answer 50

these*

Answer 51

this*

Answer 52

well i am studying physics so numbers are real things that can be measured,

Answer 53

@lgbasallote I was correcting the this in the first sentence.

Answer 54

Perhaps this quote is pertinent:
"Having to evaluate an expression of the form 0/0 is the penalty you have to pay for over-idealisation and is an indication that the treatment of the problem is at variance with nature".

Answer 55

\[ a^b = e^{b\ln a}\]
\[ 0^0 = e^{0\ln 0} = e^{0 \times \infty}\]
Indetermintae of zero times infinity ...
not sure if you can really do this ... just a thought!!