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- Why does 0. 00 have zero significant figures and why throw out the . . .
A value of "0" doesn't tell the reader that we actually do know that the value is < 0 1 Would we not want to report it as 0 00? And if so, why wouldn't we also say that it has 2 significant figures? In other words, saying something has zero significant figures seems to throw out valuable information What is the downside of handling 0 as an
- definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack . . .
If you take the more general case of lim x^y as x,y -> 0 then the result depends on exactly how x and y both -> 0 Defining 0^0 as lim x^x is an arbitrary choice There are unavoidable discontinuities in f (x,y) = x^y around (0,0)
- 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
- 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
- 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
- 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
- algebra precalculus - Prove $0! = 1$ from first principles . . .
You can also prove it by moving the space: "0! = 1" $\Leftrightarrow$ "0 != 1", which is computer notation for "0 $\neq$ 1" :-) Then it depends on what you count as "first principles" If we're dealing with the natural numbers, this follows from the Peano axiom that the successor of a natural number is not 0 (1 being defined as the successor
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