According to Deleuze and Guattari, the mathematician Riemann "uprooted the multiple from its predicate state and made it a noun, 'multiplicity'." ("Smooth and Striated": The Mathematical Model. 1000 Plateaus, pp 482-3) While some multiplicities are metric, others are non-metric. The latter are "anexact yet rigorous." Unlike magnitudes, multiplicites "cannot divide without changing in nature each time. An intensity, for example, is not composed of addable and displacable magnitudes: a temperature is not the sum of two smaller temperatures. A speed is not the sum of two smaller speeds." (see duration.)
Gilles Deleuze pits the conjunction AND to the verb IS, "to be." He describes philosophy as weighted down with attributive or existential judgements, all turning on the verb "to be." (Negotiations, p. 44) By contrast, AND is about autonomous relational judgements, not even a specific kind of relation, but all relations. AND doesn't just upset relations, it upsets being.
Multiplicity is precisely in the "and", which is different in nature from elementary components and collections of them. AND is neither one thing nor the other, it's always in between. It's the borderline, a line of flight or flow. It's the least perceptible of things. Yet it's along this line of flight that things come to pass. ...A whole micropolitics of borders, countering the macropolitics of large groups.
Deleuze rejects the Hegelian concept of desire in the service of a unified subject. For Deleuze, there is a significant difference between an internally multiplicitous desire which is unified in a structure of containment, and a fundamentally multiplicious desire which cannot be described as a unity. The notion of unity (unité) "only appears when there is a power takover in the multiplicity". The work of D & G is a ceaseless effort to disrupt that unity. Is there a relation between Deleuze's concepts and the wave of interest in multiple personalities? The multiple personality field is organized around the causal idea that multiplicity is a coping mechanism, a response to early and repeated trauma, often sexual in nature. More recently the multiplicity of personalities has been played down in favor of calling it a dissociative disorder, which is the failure of integration of various aspects of idenitity, memory, and consciousness. In the language of multiplicity, an alter is "out" when it takes executive control.