If zero (0) is added to any real number a, as a result we get a: a + 0 = a. What now was added to a? Nothing? I would say wrong. In some sense.

Namely from our friend, the set theory, point of view set A = {0} is not empty, there is something, namely number zero. If one would say, that 0 is nothing, in set A weren’t anything. In our case there clearly now is something, element 0.

Somehow philosophically 0 isn’t in same extent ”nothing”, that it would lead from view of set theory as the only element in the set to same state as the empty set ({} or ∅), that is so empty, that there simply is nothing; the empty set is more ”nothing” than 0. As  a number, zero is considered as neutral element in some cases. But it obviously is more… What?

As to empty set, more philosophical question is, does the empty set contain itself – and is it then empty.

Emptyness and nothingness have their differences.

Let us imagine an empty room where there is four walls and a roof. Emptyness gives there space. And also this emptyness, space, has many meanings; if the room has only little space you would probably feel quite uncomfortable there.

In music the fact the there isn’t a note is known as pause. In this case emptyness in the notes gives rhythm to the music, without this non-existence of a note (nothingness from point view of sound?) we would’n have music as we know it.

In speech silence, a pause, can give one some kind of power to the speech itself.

Emptyness and nothingness really are powerful from their beings!

I consider ”nothing” as something that doesn’t exist. Still it does.

Update! (16/5/2016)

In order to express all this more precisely zero is interpreted as an positive integer, but not genuinely positive integer; ”nothing” can’t be a positive integer. As to 0 + a = a, to number a is added an positive integer – something else than ”nothing”. This makes me consider the empty set being ”more nothing” than number zero. In this particular case to a is added a neutral element zero – not ”nothing”, in some sense…

It seems we’re pushing the limits of semantics of ”nothing” to new boundaries… Anyway it is essentially something else than ”emptyness”. See my post on creation.

The question now is: Is the rank of {} zero (0)? Do we need to “divide” zero; do we need a new “zero”?