<p>Abstract mathematical concepts underlie many procedures used by engineering students throughout their education. Understanding actual infinity is not only central to mastering advanced mathematical content but also crucial for developing the kind of abstract reasoning required in modern STEM education. This study examines the understanding of the concept of actual infinity among 269 mechanical engineering students. Three simple tasks related to cardinality, decimal representations, and infinite sums were used to assess students’ comprehension. Despite having completed a calculus course, students demonstrated persistent misconceptions, with accuracy rates ranging from 15.5% to 21%. Analysis of their explanations revealed a recurring tendency to replace actual infinity with potential infinity or to overgeneralize rules that apply only in finite contexts. A general tendency toward overconfidence was evident across all tasks, as many students displayed high self-assessed certainty even when their reasoning was incorrect. This pattern was especially pronounced in the Infinite Nines task, where 74.53% of participants significantly overestimated the correctness of their answers. These findings point to critical gaps in mathematics education, which often prioritizes procedural fluency over conceptual understanding. The results underscore the need for instructional approaches that place greater emphasis on abstract mathematical concepts to enhance conceptual clarity and mitigate the overconfidence that can hinder deeper learning.</p>