669 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 ...
83 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 ...
213 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, ...
179 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 ...
118 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 ...
96 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 ...
173 views

### $x^y$ for positive $x,y\ll 1$ [duplicate]

(Not a duplicate) Just playing around with a calculator (the one that comes with Windows 7), I notice that for quite small values of $x$ and $y$, $x^y$ is approximately equal to 1. Examples: ...
159 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 ...
75 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 ...
69 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 ...
112 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 $0$ ...
111 views

### What is $0^0$? Should we define $0^0$ on its correctness or convenience? [duplicate]

What is $0^0$ ? I have read many debates about this question. The debate has been going on at least since the early 19th century. At that time, most mathematicians agreed that $0^0$ = 1, until in ...
110 views

### 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 $1$.
76 views

### $0^0 = 1$ 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 $e^0 = 1$?
68 views

### Why is $0^0=1$, given the following information? [duplicate]

Why is $0^0=1$, given the following information? We really have two separate rules that are at odds with each other. Typically we have $0^n=0$ (provided n is positive) and $a^0=1$. Each of these ...

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