In the realm of mathematics, transfinite numbers are numbers that are larger than any finite number but still maintain a defined order and structure. However, in the context of atomic numbers, which represent the number of protons in an atom's nucleus, the concept of a transfinite atomic number is not meaningful within our current understanding of physics.
Our current periodic table is based on the known elements, which have atomic numbers ranging from 1 (hydrogen) to 118 (oganesson). Each element is defined by its specific number of protons. Introducing a transfinite atomic number would imply an element with an infinite number of protons in its nucleus, which is not consistent with the structure and behavior of known elements.
It's important to note that our scientific understanding and models are based on empirical observations and experimental evidence. there is no scientific basis or evidence to suggest the existence of elements with transfinite atomic numbers or atoms beyond the known range.