Adding Past Infinity (WARNING: Math Ahead)
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Suppose you add up one plus two plus four plus eight plus sixteen plus… well, youget the point. Each number is twice as big as the previous one, so it's pretty obviousthat this sum is infinite…But wait a second! We can multiply the whole thing by one and it'll be the same, right?And one is the same as two minus one… so we have two plus four plus eight plus sixteenetc., minus one minus two minus four minus eight minus sixteen…So almost everything on the right side cancels, and voila: 1+2+4+8+16, and so on, is negativeone!
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Suppose you add up one plus two plus four plus eight plus sixteen plus… well, youget the point. Each number is twice as big as the previous one, so it's pretty obviousthat this sum is infinite…But wait a second! We can multiply the whole thing by one and it'll be the same, right?And one is the same as two minus one… so we have two plus four plus eight plus sixteenetc., minus one minus two minus four minus eight minus sixteen…So almost everything on the right side cancels, and voila: 1+2+4+8+16, and so on, is negativeone!
