mathworld.wolfram.com
Zero
http://mathworld.wolfram.com/Zero.html?
19 comments
Cipher comes from the same root as Zero (sifr), making it a doublet word.
http://english.stackexchange.com/questions/30774/origin-of-z...
http://english.stackexchange.com/questions/30774/origin-of-z...
So the whole thing is a love poem then, with "cipher" actually meaning "zero", "nothing", or "negate".
Cool.
Cool.
c'mon man, put a link for that paper of yours. You know everyone here will be curious (well, at least some people will be, I'm sure).
Bill Casselman is interested in the history of the number 0, and travelled to Gwalior, India, to see one of the oldest known written occurrences of it. I had the good fortune to be eating at a dinner with him in which he was talking about his trip (see http://www.ams.org/samplings/feature-column/fcarc-india-zero), and another diner remarked, without missing a beat, "that's a long way to go for nothing."
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.
It is sad that the link to the School House Rock segment "My Hero, Zero" appears to have been hijacked.
The last good capture was in Feb 2009 https://web.archive.org/web/20090214010119/http://school-hou...
The last good capture was in Feb 2009 https://web.archive.org/web/20090214010119/http://school-hou...
It 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.
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...
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.
The real WTF in IEEE 754 is why there needs to be so many different ways to represent NaN.
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Zero: The Biography of a Dangerous Idea (Seife) is a terrific book. Highly recommended!
http://www.goodreads.com/book/show/329336.Zero
http://www.goodreads.com/book/show/329336.Zero
Wolfram'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
This is fascinating, didn't know there was such a rich history behind zero.
My final paper was a 15-20 page paper on Zero, and, despite cringing at my own writing, is still probably my favorite thing I've ever written. Zero has a fascinating history, from being outlawed in a few European countries, to being associated with the Mayan King of Death. One great little piece is the following poem:
>U 0 a 0, but I 0 thee
>O 0 no 0, but O 0 me.
>O let not my 0 a mere 0 go,
>But 0 my 0 I 0 thee so.
The word "cipher" used to be another name for zero/0, so the above reads as:
>You sigh for a cipher, but I sigh for thee
>O sigh for no cipher, but O sigh for me.
>O let not my sigh for a mere cipher go
>But sigh for my sigh, for I sigh for thee so.
Which, of course, explains why Neo, The One from the Matrix, had an enemy named Cypher.