No, atomic numbers do not rise infinitely. The atomic number of an element corresponds to the number of protons in the nucleus of an atom of that element. As of our current understanding, there is a finite number of protons in the universe, which means there is a limit to the atomic numbers of elements.
In nature, elements are identified by atomic numbers ranging from 1 to 118, corresponding to hydrogen (atomic number 1) to oganesson (atomic number 118). These elements are organized in the periodic table based on their atomic numbers and their properties.
It's worth noting that elements with higher atomic numbers are generally less stable and have shorter half-lives. Elements with atomic numbers beyond 118 are highly unstable and have been created only in laboratories as synthetic or artificially produced elements. Scientists continue to explore and synthesize these superheavy elements in experiments, but they are not commonly found in nature.
Therefore, while atomic numbers extend beyond what naturally occurs in the universe, they are not infinite and have an upper limit determined by the number of protons that can exist in atomic nuclei.