# Thread: subtraction of zero

1. ## subtraction of zero

IS THIS A NUMBER THEORY?
IS IT ALREADY KNOWN?
0 = 0 : (IS this the first known enumeration?) : +0 = 0 = +0
0 = +0 : ARE unsigned numbers are always positive ?
+0 - +0 = +0 = 0 : subtraction of same
+0 + -0 = 0 : sign exchange (needs new enumeration) : -0 = 1 = +1
then -0 = 1 and -0 = +1
then +0 = 0 and +0 = -1
+1 - +1 = +0 = 0
+1 + -1 = 0 : sign exchange (needs new enumeration) : -1 = 2 = +2
then +1 = 1 and +1 = -0
then -1 = 2 and -1 = 2 = +2
does (subtraction of zero) lead to the real integers number system?
is it something left undefineable?
it seems that the negative number is always one less than the new enumeration ... -n = abs(-n)+1

2. Originally Posted by StVie
IS THIS A NUMBER THEORY?
IS IT ALREADY KNOWN?
0 = 0 : (IS this the first known enumeration?) : +0 = 0 = +0
0 = +0 : ARE unsigned numbers are always positive ?
+0 - +0 = +0 = 0 : subtraction of same
If you are distinguishing 0, +0, and -0 as separate numbers, then you should not set 0 = +0. Rather +0 is another positive number in this case, and -0 is its negative.

You are then free to use the notation 1 instead of +0 (as long as you only do addition, no multiplication).

3. ## zero equals positive zero

it seems to me 0, +0 and -0 are not three different numbers, that they are two different numbers.
0=(0 = +0) 1=(-0 = -0)=(1 = +1)
0 and +0 are the same number, aren't unsigned numbers are always positive?
-0 seems to be the problem
can one exchange signs in this way to produce -0? and can -0 even exist?
if true, do you think this would contribute to future mathematical studies?

4. Originally Posted by StVie
it seems to me 0, +0 and -0 are not three different numbers, that they are two different numbers.
0=(0 = +0) 1=(-0 = -0)=(1 = +1)
0 and +0 are the same number, aren't unsigned numbers are always positive?
-0 seems to be the problem
can one exchange signs in this way to produce -0? and can -0 even exist?
If 0 =+0, then 0 = (+0) + (-0) = 0 + (-0) = -0, therefore also 0 = -0 = +0.
if true, do you think this would contribute to future mathematical studies?
No, it's nothing new.

5. ## Re: subtraction of zero

It is easily proved that, in any ring, including the integers, the additive identity is unique. In an "ordered ring", in which we have a notion of "positive" and "negative", that additive identity is neither positive nor negative.