Infinity is primarily a concept rather than a number, often leading to paradoxes and undefined results in mathematical equations. Discussions highlight that operations involving infinity, such as subtraction or multiplication, typically yield undefined outcomes or reinforce the idea that infinity does not behave like finite numbers. Real-world implications of infinity, such as the potential for infinite time or space, are debated, with some arguing that these concepts lack observational support. The conversation emphasizes the need to approach infinity with caution in both mathematics and physics, as it can complicate theories and lead to contradictions. Ultimately, infinity serves as a crucial yet challenging concept in understanding both mathematics and reality.