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Is zero even or odd?

G

Gactimus

Jan 1, 1970
0
I know 0 is neither negative or positive but what about odd/even? I think
it's even.

Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
 
J

Josef Moellers

Jan 1, 1970
0
Gactimus said:
I know 0 is neither negative or positive but what about odd/even? I think
it's even.

Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

As it can be divided by 2 without a remainder, it is obviously even.
 
B

BB

Jan 1, 1970
0
Josef said:
As it can be divided by 2 without a remainder, it is obviously even.

The divisor would have to be something smaller than 0 like -2.
Therefore zero is both even and negative.
 
R

Randal L. Schwartz

Jan 1, 1970
0
BB> The divisor would have to be something smaller than 0 like -2.
BB> Therefore zero is both even and negative.

This is a troll. *Negative*? Can I have some of the drug you're
smoking? :)
 
D

David C. Ullrich

Jan 1, 1970
0
The divisor would have to be something smaller than 0 like -2.

Huh? 0/2 is somehow undefined because 2 > 0? Interesting.
Therefore zero is both even and negative.


************************

David C. Ullrich
 
J

John Sefton

Jan 1, 1970
0
Randal said:
BB> The divisor would have to be something smaller than 0 like -2.
BB> Therefore zero is both even and negative.

This is a troll. *Negative*? Can I have some of the drug you're
smoking? :)

It's not a prime, because a prime can
only be divided by itself and 1.
0 can't be divided by itself, but
can be divided by everything else.
An anti-prime?
John
 
T

Tam/WB2TT

Jan 1, 1970
0
BB said:
Josef said:
As it can be divided by 2 without a remainder, it is obviously even.

The divisor would have to be something smaller than 0 like -2.
Therefore zero is both even and negative.
I seeem to recall 0 coming up negative in some old IBM mainframes. That was
an artifact of the way signed numbers were converted to binary.

Tam
 
K

keith

Jan 1, 1970
0
---
Zero has no sign. Consider:

If zero was positive, 1+0 > 1, but 1+0 = 0
If zero was negative, 1+0 < 1, but 1+0 = 0

That depends on your processor. Many FPUs have both negative and positive
zero. Even fixed point arithmetic using 1's compliment has both positive
and negative '0'. It depends what the meaning of "arithmetic" is. ;-)

Yikes! So many cross-posts to groups that apparently aren't on my server!
 
N

Nicholas O. Lindan

Jan 1, 1970
0
John Sefton said:
0 can't be divided by itself,

Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1

It works if the only three numbers in the universe are
0, 1, and infinity -- A number system that seems very
suited to usenet.
 
M

Mitch Harris

Jan 1, 1970
0
Randal said:
BB> The divisor would have to be something smaller than 0 like -2.
BB> Therefore zero is both even and negative.

This is a troll. *Negative*? Can I have some of the drug you're
smoking? :)

Well, it's called "negative" in French. (also positive, in order to
be logically consistent). And their bridges hold up pretty well.

as to the antecedent, woo hoo! I'd guess sleep deprivation.
 
J

John Woodgate

Jan 1, 1970
0
(in <[email protected]>) about 'Is zero even or odd?',
I know 0 is neither negative or positive but what about odd/even? I think
it's even.

Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

There is other evidence. Even powers of negative numbers are positive,
and (-x)^0 = 1, which is usually positive. (;-)
 
R

Richard Tobin

Jan 1, 1970
0
It's not a prime, because a prime can
only be divided by itself and 1.

If you rephrase that as "is a multiple only of 1 and itself" you will save
yourself the exception
0 can't be divided by itself

-- Richard
 
J

John Woodgate

Jan 1, 1970
0
I read in sci.electronics.design that Nicholas O. Lindan <[email protected]>
Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1

One possible solution, given the enormous lack of rigour in 'infinity'.
But in general, 0/0 can take any value. Consider:

Lim {@->0}[([email protected])/@] = 2377.pi
 
A

Androcles

Jan 1, 1970
0
John Fields said:
---
Zero has no sign. Consider:

If zero was positive, 1+0 > 1, but 1+0 = 0
If zero was negative, 1+0 < 1, but 1+0 = 0

I thought 1+0 = 1, but I guess I can't do hard sums.
Androcles.


 
A

Alec McKenzie

Jan 1, 1970
0
I seeem to recall 0 coming up negative in some old IBM mainframes. That was
an artifact of the way signed numbers were converted to binary.

In computers using ones complement arithmetic, the number zero can be
represented in two ways: all bits zero (which appears positive) or all
bits one (which appears negative).

But this is just a matter of how numbers are represented in the machine,
and says nothing about whether zero is really a positive number, a
negative number, or neither.m
 
J

Jim Thompson

Jan 1, 1970
0
Josef said:
As it can be divided by 2 without a remainder, it is obviously even.

The divisor would have to be something smaller than 0 like -2.
Therefore zero is both even and negative.

PSpice uses...

  +1 if x>0
 SGN(x) = 0 if x=0
  -1 if x<0

which matches up with what is shown on Wolfram's site...

http://mathworld.wolfram.com/Sign.html

A real royal nuisance when applying SGN(x) to system behavioral
modeling.

...Jim Thompson
 
M

Mr. 4X

Jan 1, 1970
0
BB said:
The divisor would have to be something smaller than 0 like -2.
Therefore zero is both even and negative.

Really? Is [positive number]*0 negative?
 
F

Franz Heymann

Jan 1, 1970
0
BB said:
even.

The divisor would have to be something smaller than 0 like -2.
Therefore zero is both even and negative.

Oh, dear.

Franz
 
A

Androcles

Jan 1, 1970
0
Tam/WB2TT said:
BB said:
The divisor would have to be something smaller than 0 like -2.
Therefore zero is both even and negative.

I seeem to recall 0 coming up negative in some old IBM mainframes.
That was an artifact of the way signed numbers were converted to
binary.

Tam
Not quite, but close. The ones-complement is to convert all zeroes to
one
and all ones to zero.
The twos-complement is the same as the ones-complement but then one is
added.
Thus a negative zero is created by from binary 00000000 to become
11111111 which represents -1. By adding 1, we obtain (1)00000000
and the register, being unable to hold the 9th digit, is said to
overflow,
leaving 00000000.
This is a software matter that is independent of IBM.
When the numbers are fractional, as would be needed for sines
and cosines, etc, the difference between 0.999 and 1.0 is seldom
significant, but the difference between -1 and 0 is a catastrophe.

When I was test engineering for flight simulators, the DC9 sits
on the runway with the nose pitched down by 0.5 degrees. Upon
take off, it passes through zero and the pitch becomes positive.
Exacly a zero degrees, the image flipped upside down and displayed
the runway from the tail, going away, instead of the forward view,
then flipped back to normal. Failing to use the 2's complement
was the cause.
Androcles.
 
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