Is zero even or odd?

Discussion in 'Electronic Design' started by Gactimus, Dec 20, 2004.

1. Kevin AylwardGuest

There is a lot I don't know, but this isn't an example of such.
No it isn't, it is an operator on all numbers, integer or otherwise.
Sure, you can have *another* meaning to the / operator in a different
context, but this aint that context. This discussion is about a/b as
usually understood in arithmetic.
My, my, aint you a clever dude...
Nope. I am using a well understood definition of division as applicable
to this argument.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

2. Fred BloggsGuest

We were talking about integers, and therefore 0/0={all integers}. You
want to talk about reals then 0/0={ all reals }. Are you saying that 0*x
I just told you how it is understood.
Really? You never have told us what your "well understood" definition
is- so what exactly are you "using" here?

3. John WoodgateGuest

I read in sci.electronics.design that Kevin Aylward
I don't know, but the word 'meaningless' is meaningful. I hope that is
of no help whatsoever. (;-)

6. John FieldsGuest

---

b = 1
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b = b
1+1 = 1

7. BBGuest

Well sure. 0 /+N is illogical. It's like asking:
"How many universes are in a black hole ?"
0/-N makes more sense. Therefore, black holes
have lots of useless anti-matter inside of them. ;-)

8. Nicholas O. LindanGuest

Man, like, we don' need no steenkin' facts ...

9. Nicholas O. LindanGuest

Better minds than can be found here have argued this and not reached
any conclusion. 'Undefined' is the answer given by the teacher in the
7th grade, and will serve for all practical purposes.

Maybe what is needed is a New Number = '*' (or something) = Any Number You Want.

10. Nicholas O. LindanGuest

Oh, this sounds like even more fun. Something we know even less

I would say about a black-hole's-worth.

But I don't believe in black holes.

Makes me an expert on the subject ...

11. BBGuest

How many black holes are there in the universe ?

Is it meaningful to ask infinity/0 ?

Are we going to need some kind of mathematics
where the second question is somewhat meaningful
in order to answer the first question ?

Is the last (sic) question meaningful ?
There are black holes stealing odd socks out of
my laundry.

12. Richards Noah \(IFR LIT MET\)Guest

You guys are arguing two different things. The argument that 0/0 is the set
of all integers/reals/whatever you are using is the set theory response to
the question. However, the more commonly used form is the algebraicly
accepted argument that states that division is a function of the forms: Z /
Z -> Q, R / R -> R, etc. In this definition, division by 0 is undefined for
all Z or R, including 0. So, you are both correct, but arguing different
things.

13. Steven LordGuest

Want.

Just FYI, if you're performing arithmetic using the IEEE 754 standard, then
n/0 for n not equal to 0 is the infinity with the same sign as n (i.e. -1/0
is -Inf while 1/0 is +Inf). Under the standard, 0/0 is NaN (Not a Number).

http://stevehollasch.com/cgindex/coding/ieeefloat.html

you'll see some of the operations on numbers that can be represented in the
form given by the standard that give "special" results.

Professor William Kahan also discusses some of these types of operations in
these lecture notes, starting around page 6:

http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF

14. Nicholas O. LindanGuest

Ever hear the one about the Grandmother and blowing eggs?

IEEE passed a standard. Well, heck then, the issue is settled.
Lets all go home.

An even number plus an even number equals an even number.

An odd number plus an even number equals an odd number.

An odd number plus an odd number equals an even number.

0 + 1 = odd number

0 + 2 = even number, 2 is not odd, so zero must be even.

16. Tam/WB2TTGuest

It depends on how you get there, [sin(x)]/x is certainly defined for all
values of x including 0 and infinity.

Tam

17. Chris MatternGuest

No, it most certainly is *not*. [sin(x)]/x for x=0 is
0/0 and is undefined. The *limit as x approaches 0* of
[sin(x)]/x is 1, but that's not even vaguely the same
thing. The difference is huge.
--
Christopher Mattern

"Which one you figure tracked us?"
"The ugly one, sir."
"...Could you be more specific?"

18. John W. KennedyGuest

In the days before IEEE format, at least one FORTRAN was designed to
read, write, and test equality on -0.0, so that it could be used as NaN
(usually for "datum missing"), but I grant that having a real NaN is
ever so much nicer.

19. Richards Noah \(IFR LIT MET\)Guest

(2 * 0) / 0 = (2 * 0) * (1 / 0 ) <- Definition of division as the
inverse of multiplication
(2 * 0) * (1 / 0) = 2 * (0 * (1 / 0)) <- Associative property of
multiplication
2 * (0 * (1 / 0)) = 2 * (0 / (0 / 1)) <- Definition of division
2 * (0 / (0 / 1)) = 2 * (0 / 0) <- 0 / 1 = 0

He was just leaving out some unnecessary steps, being as that they are
rather common and generally just understood.

Of course, this is following the same strange assumptions of the fact that 0
/ 0 is a defined operation, or that 0 has an inverse.

20. Nick AttyGuest

[huge cross-posting continued remorselessly - fu to rec.puzzles 'cos

Someone, and I can't remember who, once said something to the effect
that all computer programs should work like this. They should allow no
instances of something, one instance of it, or any number at all.

It's not a bad idea - think how many bugs are a result of programs
dealing with far more things than the programmer ever expected.

means anything to computers, whether C is a turing complete language
etc.