# subtraction of zero

• Jul 13th 2005, 09:01 PM
StVie
subtraction of zero
IS THIS A NUMBER THEORY?
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
• Jul 20th 2005, 07:10 AM
hpe
Quote:

Originally Posted by StVie
IS THIS A NUMBER THEORY?
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).
• Jul 21st 2005, 11:16 PM
StVie
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?
• Jul 23rd 2005, 09:22 AM
hpe
Quote:

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.
Quote:

if true, do you think this would contribute to future mathematical studies?
No, it's nothing new.
• Nov 20th 2015, 06:03 AM
HallsofIvy
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.