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请输入英文单字，中文词皆可：

0    
0
adj 1: indicating the absence of any or all units under
consideration; "a zero score" [synonym: {zero}, {0}]
n 1: a mathematical element that when added to another number
yields the same number [synonym: {zero}, {0}, {nought},
{cipher}, {cypher}]

A dictionary containing a natural history requires too
many hands, as well as too much time, ever to be hoped
for. --Locke.
0 \0\ adj.
1. indicating the absence of any or all units under
consideration; -- representing the number zero as an
Arabic numeral.

Syn: zero
[WordNet 1.5 PJC]

{zero}

0 Numeric zero, as opposed to the letter ‘O’ (the 15th
letter of the English alphabet). In their unmodified forms they look a lot
alike, and various kluges invented to make them visually distinct have
compounded the confusion. If your zero is center-dotted and letter-O is
not, or if letter-O looks almost rectangular but zero looks more like an
American football stood on end (or the reverse), you're probably looking at
a modern character display (though the dotted zero seems to have originated
as an option on IBM 3270 controllers). If your zero is slashed but
letter-O is not, you're probably looking at an old-style ASCII graphic set
descended from the default typewheel on the venerable ASR-33 Teletype
(Scandinavians, for whom Ø is a letter, curse this arrangement).
(Interestingly, the slashed zero long predates computers; Florian Cajori's
monumental A History of Mathematical Notations notes
that it was used in the twelfth and thirteenth centuries.) If letter-O has
a slash across it and the zero does not, your display is tuned for a very
old convention used at IBM and a few other early mainframe makers
(Scandinavians curse this arrangement even more,
because it means two of their letters collide). Some Burroughs/Unisys
equipment displays a zero with a reversed slash. Old
CDC computers rendered letter O as an unbroken oval and 0 as an oval broken
at upper right and lower left. And yet another convention common on early
line printers left zero unornamented but added a tail or hook to the
letter-O so that it resembled an inverted Q or cursive capital letter-O
(this was endorsed by a draft ANSI standard for how to draw ASCII
characters, but the final standard changed the distinguisher to a tick-mark
in the upper-left corner). Are we sufficiently confused yet?


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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
  • Why is $\infty\times 0$ indeterminate? - Mathematics Stack Exchange
    Your title says something else than "infinity times zero" It says "infinity to the zeroth power" It is also an indefinite form because $$\infty^0 = \exp (0\log \infty) $$ but $\log\infty=\infty$, so the argument of the exponential is the indeterminate form "zero times infinity" discussed at the beginning
  • Is $0$ a natural number? - Mathematics Stack Exchange
    Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered i
  • 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?
  • 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
  • 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
  • definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack . . .
    Why is any number (other than zero) to the power of zero equal to one? Please include in your answer an explanation of why $0^0$ should be undefined
  • 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
  • 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





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