803 views

### How to define the $0^0$? [duplicate]

Possible Duplicate: Zero to zero power According to Wolfram Alpha: $0^0$ is indeterminate. According to google: $0^0=1$ According to my calculator: $0^0$ is undefined Is there ...
715 views

### My dilemma about $0^0$ [duplicate]

We know that $0^0$ is indeterminate. But if do this: $$(1+x)^n=(0+(1+x))^n=C(n,0)\cdot ((0)^0)((1+x)^n) + \cdots$$ we get $$(1+x)^n=(0^0)\cdot(1+x)^n$$ So, $0^0$ must be equal to $1$. What is ...
143 views

### $0^0$ — indeterminate, or $1$? [duplicate]

One of my teachers argued today that 0^0 = 1. However, WolframAlpha, intuition(?) and various other sources say otherwise... 0^0 doesn't really "mean" anything.. can anyone clear this up with some ...
232 views

### Deconstructing $0^0$ [duplicate]

Possible Duplicate: Zero to zero power It is well known that $0^0$ is an indeterminate form. One way to see that is noticing that $$\lim_{x\to0^+}\;0^x = 0\quad,$$ yet, ...
188 views

### Evaluating $0^0$ and its limit [duplicate]

Possible Duplicate: Zero to zero power From what I understand $0^0$ is indeterminate, yet when you evaluate $\lim\limits_{x\to 0}x^0$ you get 1 (given on wolframalpha.com). Something ...
143 views

### Why is $0^0$ also known as indeterminate? [duplicate]

I've seen on Maths Is Fun that $0^0$ is also know as indeterminate. Seriously, when I wanted to see the value for $0^0$, it just told me it's indeterminate, but when I entered this into the exponent ...
169 views

### Proofs for $0^0 =1$? [duplicate]

Everyone knows the following: $$0^x = 0 \quad \wedge \quad x^0 = 1 , \quad\forall x \in R^*$$ One morning, I wake up asking myself the question "$\text{What is$0^0$, then?}$". So, I did what any ...
110 views

### Power series and the value of the expression $0^0$ [duplicate]

I have a doubt regarding the value of the expression $0^0$. I know this value is taken as indeterminate as far as limits are concerned. All was fine upto now. But when I encountered power series, I ...
248 views

### Why is $0^0$ undefined? [duplicate]

Possible Duplicate: Zero to zero power I'm wondering why $0^0$ is considered undefined. Why isn't 1 considered a valid solution? Considering $0^0 = 1$ seems reasonable to me for two ...
96 views

### Convergence of $\sum_{n=0}^\infty \frac{1}{n^n}$ [duplicate]

I'm stuck at deciding wether or not $\sum_{n=0}^\infty \frac{1}{n^n}$ converges.The sequence itself is a zero sequence and the root test seems to pass, but how can that be since for n=0 we would have ...
93 views

### How come 0^0 = 1 [duplicate]

Consider this: 0^0 = 1 0^1 = 0 0^2 = 0 0^n = 0 (for int n > 0) So how come 0^0 = 1, how can you get something out of ...
75 views

### What is the result of $0^a$? [duplicate]

Possible Duplicate: Zero to zero power Suppose that $0^n$ where $n$ is any natural number (or non-negative real number.). What would be the result of this calculation? Also, what would ...
123 views

### I just found out that $0^0$ equals $1$, why is this? [duplicate]

I have done a lot of math so far, but I never stumbled on something this simple and yet mind boggling. Can someone tell me why $0^0$ equals $1$? I always knew that everything raised to a power of $0$ ...
### $0^0 = 1$ or indeterminate? [duplicate]
Is $0^0 = 1$ or indeterminate? I've heard a number of conflicting answers. If it was indeterminate, how would $$e^x = \sum_{n = 0}^\infty \frac{x^n}{n!}$$ make sense since $e^0 = 1$?
### What is $0^0$? Indeterminate or 1? [duplicate]
Possible Duplicate: Zero to zero power Sorry for asking this simple question, but googling this question yields conflicting answers. Some say it's indeterminate, other's say it's $1$.