Be careful with your language here. Zero isn't defined to be even; rather, it has the property of being even by way of the definition of an even number. Usua

Be careful with your language here. Zero isn't defined to be even; rather, it has the property of being even by way of the definition of an even number. Usually, this process involves making a conjecture and then proving or disproving it. On the other hand, definitions are, well, whatever we want them to be. We can define a sheep to be woolly, and we can define a collection of crows to be a murder, but we have to justify conjectures that all sheep are black or that all corvids are crows. Think about it this way. In Scheme/Lisp, consider the notions of functions and macros. The mathematical analogue to a definition is a function; they're defined in very much the same manner, and the idea is effectively the same. Likewise, the analogue to a theorem/corollary/lemma is a macro. A theorem allows one to traverse a logical chain from P to Q very easily, and a macro allows the Schemer/Lisp hacker to abstract dull, repetitive tasks into short, succinct statements. The humdinger: the proof to a theorem is analogous to the macro expansion. :) Now, I'm hoping I'm not being too terribly nitpicky, but 1/inf does not equal zero. It's still undefined. (See also: 1/0 does not equal infinity.) This mess hinges on the idea that infinity is not a number, and in general, it holds true for the kind of real analysis one would typically learn as an undergrad.