Is there a set of all Ordinals?

Considering the vastness and complexity of the mathematical concept of ordinals, one might naturally ponder the question: "Is there truly a comprehensive set that encapsulates all ordinals?" Ordinals, by their very nature, represent a sequencing or ordering of numbers and sets, each one greater than the preceding one in a well-defined, hierarchical manner. This hierarchical structure, stretching infinitely upwards, begs the question of whether or not there exists a definitive boundary or limit to the universe of ordinals. Moreover, the exploration of the nature of infinity and the properties of infinite sets has been a central theme in mathematics for centuries. The concept of a "set of all ordinals" touches upon this profound and intricate subject, as it essentially inquires about the existence of a single, all-encompassing entity that would unite all ordinals under one umbrella. So, I pose the question anew: Does such a set truly exist, one that captures the essence of every ordinal, both finite and infinite, in a seamless and coherent manner? The answer, as with many mathematical inquiries, may lie in the depths of complex theories and proofs, yet the mere act of posing the question fosters a deeper understanding and appreciation for the beauty and mystery of the mathematical universe.