Why were infinite sets controversial when Georg Cantor introduced them?

When Georg Cantor introduced his theory of infinite sets in the late 19th century, it faced significant controversy and resistance from the mathematical community. The primary reasons for this opposition included:

• Philosophical Objections: Cantor’s work relied on the concept of "actual" infinity—the idea that infinite sets could be treated as completed, existing entities. This conflicted with the long-standing Aristotelian view that infinity should only be considered "potential" (an ongoing process of counting without end).12
• Metaphysical Concerns: Critics, most notably the German mathematician Leopold Kronecker, argued that Cantor’s theory was too metaphysical and lacked a constructive basis. Kronecker famously held that only the integers truly existed, famously stating, "God made the integers, and all the rest is the work of man".1
• Non-intuitive Results: Cantor’s proofs, such as the demonstration that some infinite sets are larger than others (e.g., the real numbers are more numerous than the integers), challenged established mathematical intuitions. Many mathematicians found these results paradoxical, as they defied the traditional understanding that infinite quantities could not be compared in size.312