Question

Why does the expression $$0^0$$ have no meaning?

Answer 1

https://cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node14.html

This might help.........:)

Answer 2

Thanks @praxer :)

Answer 3

It's the same as 0 0's multiplied together but since it's 0 0's it has no meaning.

Answer 4

I don't know if that makes any sense ^

Answer 5

How would you explain say -2 3's then @Conqueror?

Answer 6

That actually makes sense, because there is an answer to it. -2^3 = -8.

Answer 7

you cant multiply anything by 0 and have it as an answer

Answer 8

answer choices

Answer 9

if that makes sense

Answer 10

that is open to debate
it is not to my mind an interesting debate, but a debate nonetheless
some folks say it has to be 1
most say it is undetermined

Answer 11

I wonder why x^0 equals 1

Answer 12

@satellite73 in math we don't have "debates" sir :-)

Answer 13

wanna bet?

Answer 14

Not at this level then.

Answer 15

This is an elementary algebra question.

Answer 16

http://www.math.toronto.edu/mathnet/questionCorner/powerof0.html

Answer 17

Sometimes, we can argue or not argue, but if you want something consistent with the rest of the system, you just go with it.

Answer 18

Is this a serious question because it's pretty easy to answer?

Answer 19

1 = x^ a / x^a = x^(a-a) = x^0

Answer 20

That @cwrw238 is true for x not equal to 0.

Answer 21

yes - i was just answering BlackLabel's question

Answer 22

0^0 reminds me of infinity^0

Answer 23

\(\normalsize\color{black}{ \bf 0^{0}=0^{1-1}=\frac{0^{\LARGE 1}}{0^{\LARGE 1}} =\LARGE\frac{0}{0} }\)

Answer 24

but @SolomonZelman 0 has no reciprocal

Answer 25

and ?

Answer 26

So 0^0 has no meaning because division by 0 has no meaning.

Answer 27

yes, that is what I am trying to say. I am not saying it is =1.

Answer 28

yes 0/0 has no meaning so 0^0 has no meaning

Answer 29

One does have to watch practical applications. There is more than one language out there that deliberately interprets 0/0 as Unity (1). It admits that it does this. It encourages the programmer to be SURE it is clear what is going on.

Answer 30

True @tkhunny ... but given the elementary algebra definition of $$\frac{a^m}{a^n}=a^{m-n}$$ this is the best answer I have found at that level of understanding :)

Answer 31

No objection. I'm saying only that whatever argument we present, it doesn't matter a hill of beans if your programming language does something else.

Good discussion.

Answer 32

This may help:
http://youtu.be/BRRolKTlF6Q?t=6m41s

Answer 33

@tkhunny I agree with you absolutely. And that was coming up a bit in the discussion on it that I was reading. As a programmer myself, it is definitely something we need to be conscious of.

So it sounds like your question is somewhat complex,
there is a bit of discussion around the topic,
with some disagreement among math teachers and mathematicians,
(b/c you could show mathematically that it should be 1),
unfortunately I'm not finding a great explanation of why it should be undefined,
so I still can't find a convincing argument for it,
actually here's the best thing I've seen . . . .

so any number (non-zero) raised to the 0 power is 1,
and 0 raised to any non-zero power is 0,
so if we let x = 0, and follow those rules,
then we get stuck with two different answers for 0^0.
(the first line saying that it would be 1, the second saying it would be 0)
since we can't have that conflict, many say it should be undefined.
(and for what it's worth, some computer programs interpret 0^0 as 1 as well)