Oct 9 2012: If you have zero apples you do not have nothingness as you seem to have written. You have no apples in a certain volume above your hand say. If you had 1 apple it would be in that volume. Zero just says that volume is empty. The volume is real and would allow movement so cannot be nothingness. This is the same as the use of zero in 10 where is means empty column.
The above use was how zero started out in math. 0 as nothingness came later with the introduction of algebra and the number line. This appears to be a great error since nothingness is undefinable otherwise it would not be nothingness.
Oct 8 2012: I agree that when 0 is used for absolute nothingness then it is wrong.
Nothingness cannot be defined otherwise it would not be nothingness. What cannot be defined cannot be imagined and "What cannot be imagined cannot even be talked about" - Ludwig Wittgenstein.
Nothingness is an error of the mind. Therefore something must always exist.
However, mathematical 0 has various interpretations.
1) Place holder. E.g. in the number 1000 the zero's just mean this column is empty.
2) Number. E.g. 1-1=0. Could mean if you have one thing in a box and take it out then you get an empty box.
3) Nothingness. E.g. 1-1=0. Could mean if you destroy the one thing then you have nothingness in its place.
4) Limit. 0 is the limit as n gets larger and larger in 1/n.
5) Line. 0 is equidistant between -1 and 1 on the number line.
1) and 2) seem ok but 3) not so because nothingness is undefinable.
4) is not ok because you can never get to 0. So 0 as a limit is undefined. If it could be reached it would be nothingness so the same as case 3.
5) First you have to define -1 which seems a problem. It has no meaning in the physical world. Antiparticles do not anihilate to nothingness on meeting they produce energy. Also, since 0 in this case can be approached by 1/n like case 4, then it would be nothingness again so the same as case 3.
So it looks like 0 exists only in interpretations 1) and 2) where it is just a marker for an empty space or an empty column and has no connection with nothingness. Please note that an empty space allows movement and so is not nothingness.
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A reply on Conversation: Is our math wrong? Is it our assumption of zero, or absolute nothingness?
The above use was how zero started out in math. 0 as nothingness came later with the introduction of algebra and the number line. This appears to be a great error since nothingness is undefinable otherwise it would not be nothingness.
A comment on Conversation: Is our math wrong? Is it our assumption of zero, or absolute nothingness?
Nothingness cannot be defined otherwise it would not be nothingness. What cannot be defined cannot be imagined and "What cannot be imagined cannot even be talked about" - Ludwig Wittgenstein.
Nothingness is an error of the mind. Therefore something must always exist.
However, mathematical 0 has various interpretations.
1) Place holder. E.g. in the number 1000 the zero's just mean this column is empty.
2) Number. E.g. 1-1=0. Could mean if you have one thing in a box and take it out then you get an empty box.
3) Nothingness. E.g. 1-1=0. Could mean if you destroy the one thing then you have nothingness in its place.
4) Limit. 0 is the limit as n gets larger and larger in 1/n.
5) Line. 0 is equidistant between -1 and 1 on the number line.
1) and 2) seem ok but 3) not so because nothingness is undefinable.
4) is not ok because you can never get to 0. So 0 as a limit is undefined. If it could be reached it would be nothingness so the same as case 3.
5) First you have to define -1 which seems a problem. It has no meaning in the physical world. Antiparticles do not anihilate to nothingness on meeting they produce energy. Also, since 0 in this case can be approached by 1/n like case 4, then it would be nothingness again so the same as case 3.
So it looks like 0 exists only in interpretations 1) and 2) where it is just a marker for an empty space or an empty column and has no connection with nothingness. Please note that an empty space allows movement and so is not nothingness.