The Hegselmann-Krause Dynamics for the Continuous-Agent Model and a Regular Opinion Function Do Not Always Lead to Consensus

We present an example of a regular opinion function which, as it evolves in accordance with the discrete-time Hegselmann-Krause bounded confidence dynamics, always retains opinions which are separated by more than two. This confirms a conjecture of Blondel, Hendrickx and Tsitsiklis.