[gfxxxx]

Arithmetic underflow is not a bad explanation.

How you interpret is that it's pop science misinterpretation. Temperature is necessarily defined for systems in equilibrium. Systems with "negative T" aren't in equilibrium hence T isn't strictly defined.

So, what do we mean by neg T? Solutions to Boltzmann's distribution for population inversion (more electrons, say, in an excited state than the ground state).

Usually, the hotter something is, the more excited states are occupied; but in equilibrium there are always more occupied ground states.

So "hotter than any positive T" refers to "negative T"s having more excited states than positive T