We covered the concept of infinity in Philosophy, specifically the Kalam argument. It states that a true infinity cannot exist, due to the fact that, as previously stated, infinity plus one is equal to infinity. We were given a simple example to Lightning's Infinite Hotel - the example of the Infinite Library. It states that there are an infinite number of books in a library, half red and half black. The red books are removed, with a number of black books left. However, there are still infinity black books left, and thus ∞/2=∞. Thus, infinity is simply a concept, and does not truly exist. The comparisons to pi are rather pointless, as pi has a value (albeit with tens of thousands of digits after the decimal point), whereas infinity does not - Hallucination's comparison to i was more valid.
(The Kalam argument goes on to state that because of this the Universe cannot have existed infinitely, and thus there must have been a series of causes caused by a First Cause, generally attributed to God. But that's for another time.)