According to the philosophical framework established by George Berkeley, cardinal numbers are abstract entities that exist only in the mind and are used to denote the size or quantity of a collection of objects. In Berkeley's philosophy, the concept of a physical universe composed of atoms would be seen as a collection of ideas within the mind of God.
Since the concept of a physical universe composed of atoms is not directly compatible with Berkeley's philosophy, it would not be appropriate to discuss the "fit" of a Berkeley cardinal number of atoms within such a framework.
However, if we shift our perspective and consider the question from a scientific standpoint, the observable universe is estimated to contain a vast number of atoms. Current estimates suggest there are approximately 10^80 atoms in the observable universe. This estimation takes into account the known matter and energy within the universe, including galaxies, stars, planets, and other cosmic structures.
It's important to note that this estimate refers to the observable universe, which is the part of the universe that we can currently observe. The total size and composition of the entire universe, beyond our observable horizon, remain uncertain.
In summary, if we approach the question from a scientific perspective, the estimated number of atoms in the observable universe is incredibly large but finite. However, within Berkeley's philosophical framework, discussing the fit of a Berkeley cardinal number of atoms becomes a more abstract and metaphysical concept.