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Variant, v. 1, issue 2, whole no. 2, May 1947
Page 18
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May 1947 VARIANT Page 18 Or does it? Mathematicians are funny about things like that. They keep asking questions, and it's quite difficult to prove something to them. A mathematician would say something like, "Well, so far you have just been adding equal numbers. How about trying to add up numbers which keep getting smaller and smaller?" All right, let us try this series: 1 1/2 1/3 1/4 1/5 1/6 ………. To add this up is a trifle tedious, but if you try it you will find that we still end up with a number that becomes larger than any number you might name, as long as you add on enough of these diminishing numbers. That seems to clinch the argument, doesn't it? Here we are adding up numbers which get smaller and smaller, and you see that after we add up a million of these numbers we will only be adding a millionth at a time. Yet, if we keep on adding enough of them the sum will grow and grow. Which seems obvious from the idea of infinity. After all, an infinite number of anything adds up to an infinite number, no matter thin you slice it. Or does it? Maybe, just maybe, we haven't been making the numbers get smaller fast enough. What would happen if we tried it this way? 1 1 1/2! 1/3! 1/4! 1/5! ……… Where 5! (pronounced five factorial) means 5x4x3x2x1. Now this series diminishes at a quite rapid rate, because 2! is 2, 3! is 6,4 ! is 24, 5! is 120, and so on. And so, if you add up a number of these fractions, you will discover to your astonishment that the sum will never get larger than 2.71828, no matter if you keep adding terms from now until doomsday. An infinite number of objects doesn't necessarily add up to infinity, it seems. MILTON A. ROTHMAN ***************************** TO READERS OF VARIANT IN GENERAL, AND TO THE NFFF IN PARTICULAR: In the last issue of Variant (Vol. 1, No. 1) in Robert A. Madle's column, Fantaglimaerin, on page 14, the NFFF is referred to as the *%%. This is not swearing on the part of either editor or Madle, but is a typographical error caused by depressing the wrong key and by poor proofreading. We have no dislike for the NFFF, and wish them luck in all their ventures. The Editor *********************************** $$$$SUPPORT THE BIG POND FUND$$$$
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May 1947 VARIANT Page 18 Or does it? Mathematicians are funny about things like that. They keep asking questions, and it's quite difficult to prove something to them. A mathematician would say something like, "Well, so far you have just been adding equal numbers. How about trying to add up numbers which keep getting smaller and smaller?" All right, let us try this series: 1 1/2 1/3 1/4 1/5 1/6 ………. To add this up is a trifle tedious, but if you try it you will find that we still end up with a number that becomes larger than any number you might name, as long as you add on enough of these diminishing numbers. That seems to clinch the argument, doesn't it? Here we are adding up numbers which get smaller and smaller, and you see that after we add up a million of these numbers we will only be adding a millionth at a time. Yet, if we keep on adding enough of them the sum will grow and grow. Which seems obvious from the idea of infinity. After all, an infinite number of anything adds up to an infinite number, no matter thin you slice it. Or does it? Maybe, just maybe, we haven't been making the numbers get smaller fast enough. What would happen if we tried it this way? 1 1 1/2! 1/3! 1/4! 1/5! ……… Where 5! (pronounced five factorial) means 5x4x3x2x1. Now this series diminishes at a quite rapid rate, because 2! is 2, 3! is 6,4 ! is 24, 5! is 120, and so on. And so, if you add up a number of these fractions, you will discover to your astonishment that the sum will never get larger than 2.71828, no matter if you keep adding terms from now until doomsday. An infinite number of objects doesn't necessarily add up to infinity, it seems. MILTON A. ROTHMAN ***************************** TO READERS OF VARIANT IN GENERAL, AND TO THE NFFF IN PARTICULAR: In the last issue of Variant (Vol. 1, No. 1) in Robert A. Madle's column, Fantaglimaerin, on page 14, the NFFF is referred to as the *%%. This is not swearing on the part of either editor or Madle, but is a typographical error caused by depressing the wrong key and by poor proofreading. We have no dislike for the NFFF, and wish them luck in all their ventures. The Editor *********************************** $$$$SUPPORT THE BIG POND FUND$$$$
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