Let φ : G -> G' be an isomorphism of a group <G, *> with a group <G', *'>. Write out a proof to convince a skeptic that if G is cyclic, then G' is cyclic.Other than the terminology, I'm as lost as you are at this point. I may be able to explain what the question wants, but I can by no means prove it. Thus, I present the following argument.
This question is question 42. Clearly, the answer is the inverse of The Life, Universe, and Everything, or (Life, Universe, Everything)-1. After all, f-1(f(x)) = x, so the answer to the question is clearly the question of the inverse of the answer. Or something. To simplify, we can write the answer to 42 as (Death, Universe-1, Nothing). However, what is the inverse of the universe? One is immediately tempted to say either "a point" or "the multiverse." However, neither of these answers suffice. It's much like asking, "What is the opposite of a dog?" No, the answer's not cat. The answer is not-dog. Clearly, a cat is more like a dog than a not-dog is.
However, the question was not, "What is the opposite of the universe?" but rather, "What is the inverse of the universe?" If we look at the universe additively, the answer is the negative universe. This can't be correct because the universe contains equal amounts of matter and anti-matter, thus the negative universe is the same as the universe. If we look at the universe multiplicitively, we see that the inverse of the universe is (1/universe). Which leads us to a slightly different question, "What is 1 divided by the universe?" Let us explore this more deeply.
One is the concept of unity. There is only one universe, by definition. Thus, if I were to find a number to accurately describe the universe, it would clearly have to be 1, correct? But, I already showed that the negative universe = the universe, and the only number that has this property is zero. Thus, I can safely say that the numerical form of the universe is zero. Thus, 1/the universe is the same as 1/0, which is undefined. However, the limit as n approaches 0 of 1/n is infinity. But the universe is infinite (If it's not, into what is it expanding?). How can both the universe and the inverse of the universe be infinite? So the numerical value of the universe is not zero, as I had thought. Nor is it infinity, because the inverse is also infinite.
Because there is no known number d such that d and 1/d are both infinite, I find this the perfect time to introduce the much-needed concept of counterfeit numbers. Clearly, the universe is a counterfeit number. Because counterfeit numbers are produced only through division by zero, the inverse of all counterfeit numbers is zero.
Therefore the correct answer to the original question is (Death, 0, Nothing). However, zero and nothing are the same. However, because taking the inverse of counterfeit numbers is not a one-to-one operation, the universe and everything are not necessarily equivalent. This is a topic to be explored at another time.
Posted by Gallagher at September 27, 2004 11:13 PM