Between

Its meaning depends on the notation around it. The between symbol links two objects, but the assigned rule varies by field. In interval relations, it can mark intervals that cross; in constructive mathematics, where proofs show how to build an object, and pointfree topology, which studies spaces through their open sets, A ≬ B means the sets share an element.

In the 1905 geometry book Kummer’s Quartic Surface, R. W. H. T. Hudson uses ≬ between row vectors, horizontal lists of values, for their inner product: multiply matching entries and add. In 1942, Øystein Ore used it for overlapping sets in Theory of Equivalence Relations. These examples show separate conventions.

Should I use ≬ for an interval?

Use it only after defining it. In ordinary interval notation, 2 < x < 4 leaves both endpoints out, while 2 ≤ x ≤ 4 includes them. The symbol ≬ alone does not tell readers which case you mean.