The Missing MillionDate: 06/11/2001 at 11:50:24 From: Aden Ali Subject: Addition and subtraction If I have six million dollars and my friend has three million dollars, I am wealthier than my friend by three million dollars. If I give my friend one million dollars, the latter's fortune jumps up to four million and mine comes down to five million. This means that I am now wealthier than my friend by only one million. Since I was wealthier than my friend by three million dollars before the transaction, shouldn't I be still wealthier than him by two million after giving him only one million dollars? What happened to the million dollars that is missing from me? Many people told me that my one million should be counted twice, i.e. once as a credit for my friend, and secondly as a debit to my account. I am not convinced by this answer and my children keep on asking me. Please help. Thanks. Date: 06/11/2001 at 13:14:43 From: Doctor Peterson Subject: Re: Addition and subtraction Hi, Aden. Your friends are right. Try picturing it in terms of water rather than money: I have 6 ounces of water in a glass, and by son has 3 ounces. I pour 1 ounce from my glass to his. Now I have 5 and he has 4; the difference has been reduced from 3 to 1, because _I_ have one less and _he_ has one more. The difference has been reduced on BOTH ENDS, so it decreased by twice the amount I poured. |<-------3------->| him me +-----+-----+-----+-----+-----+-----+-----+ +---->| |<----+ him me |<-1->| Does that help? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 06/12/2001 at 02:45:18 From: aden m. ali Subject: Re: Addition and subtraction Dr Math, I thank you for your kind answer to my question. The water made it simpler, although an unanswered question still looms in my son's mind, i.e. "why should you count his gain to me?" Again, many thanks for your help. Aden Date: 06/12/2001 at 08:37:06 From: Doctor Peterson Subject: Re: Addition and subtraction Hi again! It sounds as if he is forgetting the question, which is about the DIFFERENCE between two people's wealth (or water glasses), not the INDIVIDUAL amounts. The difference is affected by BOTH amounts; it is increased by "my" wealth, and decreased by "his" wealth. If my wealth decreases and his increases, then both changes decrease the difference, regardless of whether his gain comes from me or from elsewhere. We are not counting his gain toward me, only toward the difference between us. As my picture illustrated, we can model this not only in terms of money or water, but of position. If I move a centimeter to the left and he moves a centimeter to the right, then the distance between us decreases by two centimeters. Here, I can't say I'm giving him a centimeter, but the effect is the same. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 06/13/2001 at 07:08:14 From: aden m. ali Subject: Re: Addition and subtraction Dr. Math, I am very grateful for your quick answer and your kind attention. Thank you. Aden |
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