# Is zero even or odd?

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

Yes!

2. ### George CoxGuest

And two isn't prime because it's even?

3. ### Franz HeymannGuest

'infinity'.

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

[snip]

Franz

4. ### Franz HeymannGuest

[snip]
Not on my Casio calculator.

Franz

5. ### David KastrupGuest

Well, and in the above it takes on 1, so that would be quite legal,
right?

6. ### Hue-BondGuest

Shawn Corey, [email protected]:43:59(CET):
That could be said louder, but not clearer .

7. ### David KastrupGuest

What else is it there?

8. ### Alfred Z. NewmaneGuest

I'm sorry, sir, but 0 is universally defined in math to be neither - nor
+, it's jsut 0. Many graphing and soem scientific calculators have a
sign function. On any calc I've tried this on, it gives -1 for any
negative number, it gives a 1 for ant positive value, and 0 (zero) for,
well, 0 (zero.) As is defined in basic math.

9. ### Alfred Z. NewmaneGuest

Except for the fact that: 0 / 0 = undefined

Or actually more correct: n / 0 = undefined

10. ### Alfred Z. NewmaneGuest

n / 0 = undefined

11. ### Shawn CoreyGuest

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

What could be clearer?

--- Shawn

12. ### Jim ThompsonGuest

I remember that one from when I was in high school ;-)

...Jim Thompson

13. ### Fred BloggsGuest

It's a number theoretic definition- we are not talking physics and there
are no laws to invoke here. Even/odd is partition of the set of integers
in accordance with modulo-2 equivalence classes: EVEN={m: m MOD 2=0} and
ODD=INTEGERS-EVEN. The set of even numbers is all integers of the form
2n, everything else is odd.

14. ### Nicholas O. LindanGuest

Now if we can just get the IRS to agree.

15. ### Fred BloggsGuest

0/0={ SET OF ALL INTEGERS }

n/0= NULL SET for n<>0

It is very well-defined.

16. ### Alfred Z. NewmaneGuest

No, it's just 9. You dont have +0 or -0, it's just 0 (zero.) Writing it
as +0 or -0 still is jsut 0 sicne 0 has no sign. You have +, -, and 0.
Or for what you get from any proper sign function, either 1, -1, or 0.

17. ### Alfred Z. NewmaneGuest

Thats becuase, when translated to reality, that statement becomes (0)^2
= 0, because 0 has no sign. I really wish people would stop trying to
spread the false hood that0 actually has a sign.

18. ### Jim WardGuest

0 has no flat edges, so it can't be even.

19. ### Richard TobinGuest

No, you *do* have +0 and -0, and they are both equal to 0.

-- Richard

20. ### Ed MurphyGuest

I used to know a proof along these lines:

-----

x = +1
A = [integral] f(x) dx
x = -1

By examining a graph, it is obvious that A > 0.

Let y = 1/x, therefore x = 1/y, and substitute this into the equation:

x = +1
A = [integral] f(1/y) f'(y) dy
x = -1

The right-hand side is clearly equivalent to -A

A = -A

A = 0