安裝中文字典英文字典辭典工具!
安裝中文字典英文字典辭典工具!
|
- 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
- Zero power zero and $L^0$ norm - Mathematics Stack Exchange
This definition of the "0-norm" isn't very useful because (1) it doesn't satisfy the properties of a norm and (2) $0^ {0}$ is conventionally defined to be 1
- 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
- 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
- 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
- complex analysis - What is $0^ {i}$? - Mathematics Stack Exchange
0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0 On the other hand, 0−1 = 0 0 1 = 0 is clearly false (well, almost —see the discussion on goblin's answer), and 00 = 0 0 0 = 0 is questionable, so this convention could be unwise when x x is not a positive real
- Why Not Define $0 0$ To Be $0$? - Mathematics Stack Exchange
That $0$ is a multiple of any number by $0$ is already a flawless, perfectly satisfactory answer to why we do not define $0 0$ to be anything, so this question (which is eternally recurring it seems) is superfluous
- Why I cant calculate $0*log (0)$ but can $log (0^0)$
If you need to calculate $0 \log 0$, you're probably either: Doing something wrong Implementing an algorithm that explicitly states that $0 \log 0$ is a fib that doesn't mean "compute zero times the logarithm of zero", but instead something else (e g "zero") If $\log 0^0$ worked in your programming language, it's probably because it used the "wrong" exponentiation convention, and returned $0
|
|
|