The concept of "infinitely small" is a topic that has been explored in mathematics and physics, but it is not a well-defined notion in the context of our current understanding of the physical world.
In classical mathematics, the concept of infinitesimals was used in the development of calculus. Infinitesimals were treated as quantities that are smaller than any real number but still nonzero. However, this approach was later formalized and replaced by the concept of limits, which avoids the need for explicitly considering infinitely small quantities.
In modern physics, our understanding of the physical world is based on quantum mechanics and relativity. In quantum mechanics, the behavior of particles is described using wave functions and probabilities, and there is a fundamental limit to the precision with which certain physical properties, such as position and momentum, can be simultaneously known. At extremely small scales, such as the Planck length (about 1.6 x 10^(-35) meters), our current theories break down, and we do not have a complete understanding of the underlying physics.
In the framework of general relativity, which describes the gravitational interactions on a large scale, spacetime is smooth and continuous. However, at the smallest scales, such as those near a black hole's singularity or in the early stages of the Big Bang, the effects of quantum mechanics are expected to become significant, and the smoothness of spacetime might break down. Yet, the specific behavior of spacetime at such scales is still an active area of research and remains uncertain.
In summary, while the concept of "infinitely small" has been considered in mathematics and has historical significance in the development of calculus, it is not well-defined in our current understanding of the physical world. The behavior of the physical universe at extremely small scales is an area of ongoing research and is subject to the limitations and uncertainties of our current theories.