[isanengineer]

Good point. I think the what's missing is how electron energy states work in quantum mechanics. The wikipedia paged (linked below) has a pretty good explanation:

"A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized". (https://en.wikipedia.org/wiki/Energy_level)

To put things another way: while there could theoretically be infinite sizes of energy quanta, the permutations of energy states for matter are in fact discrete.

Disclaimer: I am an engineer, not a physicist.

[kergonath]

What you say is true, but also incomplete. We are perfectly able to quantify the accessible states in purely classical systems, such as ideal gases, without requiring discrete energy levels. The trick is to think of a continuous probability density instead of discrete probabilities. This framework is very general and does not depend on the quantum-ness of what you look at.

Even in some systems that actually follow quantum mechanics (such as phonons or electrons in a material, or photons in a black body), we often use continuous probabilities (densities of states) because it’s much more convenient when you have lots of particles.