Is zero even or odd?

[YD]

I read in sci.electronics.design that Nicholas O. Lindan <[email protected]>


I've seen v/(x) used; it's fairly evident what it means. I just found
that decimal 175 is an 'overscore' character, ¯, which means that v/¯(x)
could be used.

Not all newsreaders or fontsets may be able to render that correctly.
Though I doubt anyone is still using 7-bit ASCII.

How about) for cube root?

There, you see? It became a ) for me.

- YD.

 

[Bill Smythe]

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

Of course it is. There exists a whole number X such that X*2=0. Thus, 0 is
even.

Bill Smythe

 

[vonroach]

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

Er..., it can also be divided by every other number (rational,
irrational, and imaginary) without a remainder, although some of us
are amused by the strange concept of dividing nothing and the absurd
idea that there may be a `remainder'. Then comes the wild assertion
that when a number is divided by nothing, it becomes infinite.

 

[vonroach]

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

Whoa! A new concept: -0. Let's make up some other numbers. I suggest
wizzad and fugawe. I'd have suggested Arunda, but I believe some
obscure African group already uses that in their alphabet.

 

[vonroach]

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

That's no good Randy, no matter how much you buy, you still have
nothing. Coincidentally with constant use the measurable IQ approaches
zero as a limit.

 

[vonroach]

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

Perhaps a superprime. `antiprime' is as mysterious as - 0.

 

[vonroach]

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.

Add to that the troubling thought that 1/0, 1/1, 0/1, and 0/0 are all
rational numbers. If 1/0 = `infinity' how do we decide if there is any
remainder? Looks like there should be a remainder of 1. If that is so,
how do we know it has really been divided by 0?

 

[vonroach]

There is no lack of rigour in the definition of infinity. Read anbout
the work of Cantor, Dedekind and others.

Do you have similar `readings' covering 0?

 

[vonroach]

Zero is even. You cannot divide by zero. Limits are not division.
Infinity is not a number. Computers bugger up the system.

--- Shawn

Shawn, I am equally convinced that it is neither even or odd. Though I
will admit that those who need to decide are rather odd.

 

[vonroach]

Except for the fact that: 0 / 0 = undefined

Or actually more correct: n / 0 = undefined

Really, Al Z? Where did you get that doctorate in math? Various
middle eastern types have worked hard to see that was not the case.

 

[vonroach]

0/0={ SET OF ALL INTEGERS }

n/0= NULL SET for n<>0

 

[vonroach]

No it isnt.

Kevin Aylward

Now that you are in to definitions, what does `Aylward' mean?

 

[vonroach]

You apparently have stumbled on something else you know damn little
about. In case you need help with this , you might note that "/" is NOT
an operator on the integers, it is the "inverse" of a multiplication
operator. Inverse is a well-defined concept but not necessarily a
function, it is a set theoretic mapping. E.G. m/n={ q: m=q*n} by
definition, so that m/n which is actually a set which can be empty, a
singleton, or infinite. In the case of m/n, it is then m/n = F^-1(m)
where F(x)= n*x. Your reasoning would lead one to believe /: I x I -> I
is a function, which it isn't.

Ah, the inverse , like 1/0 is inverse of 0/1? Is 0/0 the inverse of
0/0? And 1/1, the inverse of 1/1.

 

[vonroach]

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.

a/b ? Now your getting into complicated stuff.

 

[vonroach]

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.

Then infinity is undefined?

 

[vonroach]

Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?

(2 x0)/0 = 2x(0/0) . there now is that better?

 

[vonroach]

If I treat 0 as an imaginary number

Now you say 0= -1^1/2? You are using your imagination.

 

[John Woodgate]

I read in sci.electronics.design that Franz Heymann <notfranz.heymann@bt

There is no lack of rigour in the definition of infinity. Read anbout
the work of Cantor, Dedekind and others.

Indeed: I was referring to the lack of rigour in '1/0 = infinity'.

 

[Nicholas O. Lindan]

Now you say 0= -1^1/2? You are using your imagination.

No, I think you are the first to say that, at least in this thread.

There are more imaginary numbers in the usenet than are counted
in your philosophy.

 

[robert j. kolker]

Er..., it can also be divided by every other number (rational,
irrational, and imaginary) without a remainder,

irrelevent. The -definition- of an even integer is an integer equivalent
to zero mod 2. Given any integer k != 0 we can always find an even
multiple of k. We can also find an odd multiple of k.

Bob Kolker