The Distinction between empty and Emptiness is all that is necessary to construct traditional mathematics.
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BRICKEN, William, 1986. A Simple Space. Advanced Decision Systems. 1986. pdf [Accessed 15 December 2023].
There are two kinds of void [⇒ The Two Voids]. The Absolute Void is simply not available to contemplation. It is Emptiness. The Relative Void is indirectly accessable, at least to thought. It is Empty Space.
The word emptiness is a noun, it refers to the Absolute Void, a state with no properties. The word empty is an adjective, it identifies the only property of the Relative Void.