Law of non-contradiction applied to zero?

Question

Consider
0 = c

This means:
- 0 = - c

But
- 0 = 0

Therefore c = - c

Isn't this in opposition with the law of non-contradiction which states that c = c ?

"One cannot say of something that it is and that it is not in the same respect and at the same time." Aristotle.

Should zero actually have a rational existence?

Answer 1

No, it is not in opposition. 0 is just the only value in standard arithmetic for which "c" and "-c" refer to the same entity.

Just because c = c, the law of non-contradiction doesn't prevent c from being equal to something else too.

For instance, in "mod 10" arithmetic, 1=11. This does not oppose the law of non-contradiction, because it's still the case that 1=1.

Answer 2

No there is no contradiction here. It is okay for c to equal its own negative because in the very beginning you told me that c IS zero.

Now if your first line was let c=1, and THEN you showed me that c=-c, then we would have a problem.

And what do you mean by zero having rational existence? That sounds like a philosophical question to me. It doesn't even belong in math.

Answer 3

The law of non-contradiction is indemonstrable (neither verifiable nor falsifiable) in that anyone who attempts to disprove it must use the law itself, and thus beg the question. In this way it can be said to be undeniable, that is, literally impossible to deny. The law is impossible to prove for the same reason, since one has to use the law to prove the law, and this is a circular argument.

So what does the law of contradiction really say and how can it really be used? Is your assertion correct or not? Seems like you could discuss this forever and get nowhere.

Answer 4

The problem with your arguement is that it has NO CONTRADICTION!.

WHy? Because your 'c' is actually '0'. And -0 = 0 by definition and meaning. So if 'c' is '0', then -0 = 0 is just as equivalent to writing ( with different symbols now to represent zero by c ) we get : -c = c.

Enjoy. :)

Answer 5

It'd be better if you could use easier words because you're getting me screwed up here.

Whatever you're talking about...

c = 0

-c = 0

0 = 0

This is true.
____________________________

Now let's take x = 1

x^2 = 1

(-x)^2 = 1

(x)^2 = (-x)^2

Is this false? No.

Perhaps 1 shouldn't be a number? NO!
____________________

Want to erase the entire number line?

x^2 = (-x)^2

x = ...-3, -2, -1, 1, 2, 3, 4, 5, 6...

POOF! You probably don't even know what numbers are now =D.