Provide a detailed exploration of the concept of infinity in mathematics, beginning with its historical development from ancient to modern times. Explain Cantor's revolutionary work on different sizes of infinity and the development of transfinite arithmetic. Discuss the continuum hypothesis and its independence from the Zermelo-Fraenkel axioms of set theory. Examine the philosophical implications of mathematical infinity and debates about whether mathematical objects exist independently of human thought (platonism) versus being constructed (constructivism). Conclude with a discussion of how infinite concepts relate to practical mathematics and the foundations of calculus.