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- What is $0^ {i}$? - Mathematics Stack Exchange
It is possible to interpret such expressions in many ways that can make sense The question is, what properties do we want such an interpretation to have? $0^i = 0$ is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention $0^x = 0$ On the other hand, $0^ {-1} = 0$ is clearly false (well, almost —see the discussion on goblin's answer), and $0^0=0
- Is $0$ a natural number? - Mathematics Stack Exchange
Inclusion of $0$ in the natural numbers is a definition for them that first occurred in the 19th century The Peano Axioms for natural numbers take $0$ to be one though, so if you are working with these axioms (and a lot of natural number theory does) then you take $0$ to be a natural number
- Is $0^\infty$ indeterminate? - Mathematics Stack Exchange
Is a constant raised to the power of infinity indeterminate? I am just curious Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
- algebra precalculus - Zero to the zero power – is $0^0=1 . . .
@Arturo: I heartily disagree with your first sentence Here's why: There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer) For all this, $0^0=1$ is extremely convenient, and I wouldn't know how to do without it In my lectures, I always tell my students that whatever their teachers said in school about $0^0$ being undefined, we
- I have learned that 1 0 is infinity, why isnt it minus infinity?
@Swivel But 0 does equal -0 Even under IEEE-754 The only reason IEEE-754 makes a distinction between +0 and -0 at all is because of underflow, and for + - ∞, overflow The intention is if you have a number whose magnitude is so small it underflows the exponent, you have no choice but to call the magnitude zero, but you can still salvage the
- Show that ∇· (∇ x F) = 0 for any vector field [duplicate]
Show that ∇· (∇ x F) = 0 for any vector field [duplicate] Ask Question Asked 9 years, 7 months ago Modified 9 years, 7 months ago
- Justifying why 0 0 is indeterminate and 1 0 is undefined
In the context of limits, $0 0$ is an indeterminate form (limit could be anything) while $1 0$ is not (limit either doesn't exist or is $\pm\infty$) This is a pretty reasonable way to think about why it is that $0 0$ is indeterminate and $1 0$ is not However, as algebraic expressions, neither is defined Division requires multiplying by a multiplicative inverse, and $0$ doesn't have one
- Seeking elegant proof why 0 divided by 0 does not equal 1
The reason $0 0$ is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals It is perfectly reasonable to contemplate particular vales for $0 0$ and obtain a contradiction This is how we know it is impossible to define it in any reasonable way
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