I know of an easier explanation on why a^0 (with a != 0) is 1. It is because a^0 = a^(n-n) = a^n / a^n = b/b = 1.
Zero
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Re: Zero
#12It is the only integer (and, in fact, the only real number) that is neither negative nor positive.
Yet in the IEEE 754 standard there is both a negative and a positive zero. They produce "true" when compared for equality but they usually produce differently signed infinities when divided by.
Re: Zero
#13It is the only integer (and, in fact, the only real number) that is neither negative nor positive. Yet in the IEEE 754 standard there is both a negative and a positive zero. They produce "true" when compared for equality but they usually produce differently signed infinities when divided by.
That makes complete sense when you consider that IEEE 754 is all about approximating values, though. It is possible that the value you're trying to represent is smaller than the smallest values actually representable by IEEE 754 floating point, but it would be nice if you could at least preserve the sign information (so that, as you point out, dividing produces the correct `Inf` value).
The real WTF in IEEE 754 is why there needs to be so many different ways to represent NaN.
Re: Zero
#14It is the only integer (and, in fact, the only real number) that is neither negative nor positive. Yet in the IEEE 754 standard there is both a negative and a positive zero. They produce "true" when compared for equality but they usually produce differently signed infinities when divided by.
That makes complete sense when you consider that IEEE 754 is all about approximating values, though. It is possible that the value you're trying to represent is smaller than the smallest values actually representable by IEEE 754 floating point, but it would be nice if you could at least preserve the sign information (so that, as you point out, dividing produces the correct `Inf` value). The real WTF in IEEE 754 is wh…
What other way is there than all ones exponent and non-zero significand?
Re: Zero
#15Wolfram's MathWorld seems dead-set on broadcasting a lie about 0^0. It is, in fact, defined to be 1. If it were undefined, then the Maclaurin series for e^x, e^x=sum_{n=0}^{infty}x^n/n!, would be undefined at x=0, but this series is universally understood to be defined for all real x.
Re: Zero
#16Earlier quoted context omitted.
That makes complete sense when you consider that IEEE 754 is all about approximating values, though. It is possible that the value you're trying to represent is smaller than the smallest values actually representable by IEEE 754 floating point, but it would be nice if you could at least preserve the sign information (so that, as you point out, dividing produces the correct `Inf` value). The real WTF in IEEE 754 is wh…
What other way is there than all ones exponent and non-zero significand?
I think parent meant the many different ways to be non-zero.
Re: Zero
#17Wolfram's MathWorld seems dead-set on broadcasting a lie about 0^0. It is, in fact, defined to be 1. If it were undefined, then the Maclaurin series for e^x, e^x=sum_{n=0}^{infty}x^n/n!, would be undefined at x=0, but this series is universally understood to be defined for all real x.
I think Knuth cleaned up the definition of 0^0, and showed that it should be 1 for consistency with a whole lot of other series' and function definitions
Re: Zero
#18Wolfram's MathWorld seems dead-set on broadcasting a lie about 0^0. It is, in fact, defined to be 1. If it were undefined, then the Maclaurin series for e^x, e^x=sum_{n=0}^{infty}x^n/n!, would be undefined at x=0, but this series is universally understood to be defined for all real x.
I think Knuth cleaned up the definition of 0^0, and showed that it should be 1 for consistency with a whole lot of other series' and function definitions
see this Quora article
http://www.quora.com/What-is-0-0-the-zeroth-power-of-zero
Re: Zero
#19Re: Zero
#20It is the only integer (and, in fact, the only real number) that is neither negative nor positive. Yet in the IEEE 754 standard there is both a negative and a positive zero. They produce "true" when compared for equality but they usually produce differently signed infinities when divided by.
Signed zero is crucial for handling branch cuts in complex functions - http://port70.net/~nsz/articles/float/kahan_branch_cuts_comp...