September 22, 1998

2 + 2 = 5

Assuming that all operations (plus, minus, multiplication, etc.) function regularly, prove
2 + 2 = 5

Solution:
Now, for those of you who hate math, this should be relatively easy if you're a smartass. Quite simply, the proof is

The question, however, is what does this mean? Some would say this implies that all you do is swap around 4 and 5 wherever either appears. The problem here is that it doesn't really explain what is happening. A more concise proof would be to say that the counting sequence of positive numbers is

We're not actually swapping numbers, we've completely rearranged the way we count. The reason we can do something so irregular is based upon a notion most people fail to comprehend. Numbers, like the x and y of high school algebra days, are variables of a sorts. They symbol 2 (yes, it is a symbol) is normally interpreted to mean (if you count how many stars) * *. 3 usually symbolizes * * *, 4 * * * *, and so on. Yet, these are symbols, so we can adjust what they stand for. If we treat 5 and 4 as variables, we just define

When we talk about numbers, we usually imply the symbols. However, the true essence of number is some arbitrary line we use to distinguish different counts, but the counts themselves. To say 2 + 2 = 5 is just as right to say 2 + 2 =4, it just all depends on your symbols.