The law of the excluded middle states that A or not A must be true. I think the law of non-contradiction states that there can be only A or not A. I might have them mixed up.
You stated something like nothingness is equal to not nothingness.
Taking this idea to a number line, we can have the set zero, which is a closed dot at zero. Let's call this N. We can have the set not zero, which is the entire number line shaded but with an open circle at zero. This is the set not N.
N and not N is the entire number line.
It's clear N and not N aren't the same. We cannot say they are equal. Using set theory notation:
N is not not N
N and not N is everything (universal set)
N intersect not N is {} (empty set)
Does N = {}?
It seems to, but I won't say for sure. That one is above my pay grade.