According to our current understanding of physics and chemistry, the number of chemical elements cannot continue indefinitely. The elements are organized in the periodic table based on their atomic number, which corresponds to the number of protons in the nucleus of an atom. there are 118 confirmed elements.
The elements beyond atomic number 118, such as oganesson (Og), have been synthesized in laboratories but are highly unstable and decay rapidly. These superheavy elements are generally produced through nuclear reactions by bombarding heavy nuclei with other particles. Due to their instability and short half-lives, they are extremely challenging to study and characterize.
As we move to higher atomic numbers, the nuclei become larger and more unstable due to the increasing number of protons. The electrostatic repulsion between protons makes it difficult for the nucleus to hold together, leading to a high degree of instability. Theoretically, there may be an "island of stability" at even higher atomic numbers, where the nuclei could be more stable due to a balance between protons and neutrons. However, reaching and studying these elements is currently beyond our technological capabilities.
It's important to note that scientific knowledge can evolve over time, and new discoveries could potentially change our understanding of the limits of the periodic table. However, based on our current understanding, there is no indication that the number of chemical elements can continue indefinitely.