Can a Single Particle Have a Temperature?

Shrinking the sample space to B and dividing by P(B) look like different operations. A dice example, a uniqueness argument and a rejection-sampling proof show they are the same one.

Latent heat keeps an ice bath at 0 °C, but air gaps and a thin water layer can waste that advantage. Here is how to set up the bath, and what nobody has measured yet.

Natural density says numbers below any fixed bound are negligible. Countable additivity says you still cannot draw one uniformly. Here is where the two separate.