# Is zero even or odd?

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

1. ### vonroachGuest

No it is meaningless gibberish.

2. ### vonroachGuest

Confused is too mild a term. If y = 1/x. then y goes from1 to a very
small fraction as x increases from 1. If x decreases to small
fractions, then y increases. x=0 yields a meaningless result.

3. ### vonroachGuest

There isn't one. Division by 0 is meaningless.

4. ### vonroachGuest

Both are meaningless. Just crap piled higher and deeper as in Ph D.

5. ### Michele DondiGuest

Wow! We started from the trollish "Re: Is zero even or odd?" and now
we're arriving to Lie (news)groups...
;-)

Michele

yes

7. ### vonroachGuest

x^0 = 1 except when x=0 which doesn't exist.

8. ### John FieldsGuest

---
And there's the rub! My point is that it _should_ be defined, and
defined like this:

0 1
--- = 1, --- = oo,
0 0
---
---
I disagree.

If we say

x
y = lim --- = 1
x +oo -> -oo x

Then y will be equal to 1 for every instance of x except when x
crosses over from + to -?

In my view that's preposterous, and the mere parroting of "division by
zero is disallowed because it's undefined" a convenient dodge. No
insult intended.[/QUOTE]

It is desirable for mathematics not to allow two contradictory
statements such as 0/0=1 and 0/0=2 to be true at the same time; and your
resoning allows these statements to be true in some cases (we did this
in the Ohm's law episode, where you never said my reasoning was wrong,
it was merely not the thing you wanted to prove).[/QUOTE]

---
Actually, what I didn't want to do was to get into a long, off-topic
harangue about Ohm's law (Ohm's formula, actually. Ohm's law is an
entirely different thing and is used to determine whether conductors
are 'Ohmic'. That is, if their resistance remains constant when
current through them is made to vary), which requires that for
resistance to be _measured_ a known voltage _must_ be placed across it
and the resulting charge flowing through the resistance determined.
Your example eschewed the _practical_ requirements in order to
contrive a desired outcome and, as such, was irrelevant.

But, proceeding along that tack for a while, maybe we can use our
"exquisite" technology to advantage here by assuming that we have
managed to craft two identical zero ohm resistors (superconducting, if
you like) and that we can force equal numbers of electrons through
each of them in equal amounts of time. Then, since Q = It, the
current flowing in each resistor will be I = Q/t, and the ratio of the
currents will be I1/I2.

Since Q/t will be identical for both resistors, I1/I2 will be 1 for
any current. Now, let's say that we inject fewer and fewer pairs of
electrons per unit time into the 'rig' and that eventually we inject
none. Since we have agreed that as long as I1=I2 then I1/I2 will be
equal to 1, does 0/0 not satisfy that requirement?
---

9. ### George DishmanGuest

I'll take that as a "No" then.

George

10. ### George DishmanGuest

[/QUOTE]

That is incorrect, multiplication and division
are of equal precedence.
Not at all. I have avoided writing this as a limit
Let

k*x
y(x) = ---
x

Clearly y(x) = k for all non-zero finite values of x and

limit y(x)
x->0 ---- = k
x

By your argument that the limit can be used to
define the value at zero, we can infer:

y(0)
---- = k
0

but of course y(0) = 0 hence

0
--- = k
0

for all finite k.

George

11. ### David KastrupGuest

And that's nonsensical.

It gives us, for example,
1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2

Well, so you are talking inconsistent nonsense. You must not expect
that it will impress anybody much.
This notation is complete and utter meaningless hogwash. What you
_can_ say is that

lim (x->v) (x/x) = 1

for _all_ v in R (and actually also if v is +oo or -oo, which is not a
number, but a neighborhood in some sense of the word).

But you can equally well say that

lim (x->v) (2*x/x) = 2

for _all_ v in R. For v=0, both limits are of the _form_ 0/0, and
that means that any such limiting _form_ is undefined without further
qualification. But you don't need limiting arguments to show that 0/0
can't be defined: mere algebra is sufficient.
to it is likely to be rubbish too.
Well, not being able to choose a consistent value is _the_ perfect
reason for leaving it undefined. You call it a dodge, other's call it
a necessity.

12. ### John WoodgateGuest

I read in sci.electronics.design that John Fields <[email protected]
I think this thread has shown that there are two sorts of people, those
that associate taboos with 0 and those that don't.

My view is that logically-inferred values of expressions involving zero
should be accepted unless they result in contradictions. I do not
support a priori restrictions on interpretation, and I do not accept
that 'undefined' is a valid show-stopper.

13. ### John WoodgateGuest

I read in sci.electronics.design that George Dishman
Yes. John Fields' value of 1 is just ONE valid solution. Not wrong, but
not the whole solution.

14. ### John WoodgateGuest

'Undefined' is a human artefact. Anything can be defined; if the
0/0 can't be *defined* as 1 because, as has been repeatedly
demonstrated, that definition results in contradictions, such as the one
illustrated above.

The only definition that does not result in contradictions is that 0/0
is 'any number'. 1 is just one solution.

15. ### John FieldsGuest

---
I thought that by interspersing your remarks among mine you were being
arbitrary. I see now that wasn't the case; thanks.
---
---
I disagree. All I was trying to do was to set up the initial
conditions to give me an equal numerator and denominator as a starting
point for a proof that, eventually, 0/0 = 1.
---
---
0/0 would still be = 1 but yes, of course, to the rest of it. A
_measurement_ would be impossible without a known, non-zero voltage
forcing charge through the resistance.
---
---
Yes, thanks.
---
---
OK, but it seems to me that if you subscribe to

2r
x = lim ---- = 2
r->0 r

when r = 0, then 0/0 _must_ be equal to 1, otherwise x could not have
been equal to 2. That is, if r/r = y and 2y = 2, then y = 1.
---
---
Because it doesn't?

In the latter case we're trying to determine whether, when equal
quantities are divided into each other, the result will always be
equal to 1, while in the former we're dealing with with the interplay
between physically different entities. I.e., 1 apple/1 orange = ???

16. ### Matthew RussottoGuest

So what do you do when there are multiple logically-inferred values,
as with 0^0? Or when the logically-inferred value breaks a lot of
other things, as with 0/0.

BTW, what's log 0? arctan 0?

17. ### John FieldsGuest

---
In the context of the problem at hand, the definition of division
isn't in question. What's being discussed is whether zero, being
equal to itself will yield a quotient of 1 when it's divided into
itself. As for the rest of it, I will follow the advice you proffer
in your dotsig and forego arguing with you.

20. ### George CoxGuest

No 0/0 is undefined, it has _no_ value.