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Question
Hi there,

This is just a question and has no basis in reality. This question may sound weird, but I hope you won't laugh at it.

For example, in a family a person dies. There are four people who are controversial about the age when he died. I mean to say that there is a difference of opinion that what was his age when he died.

1) His oldest son says that he died at the age of 70.

2) His brother says that he died at the age of 73. (This is the correct one)

3) His cousin says that he died at the age of 75.

4) His sister says that all of them are right because she has "rounded off" all of their statements.

My question is: According to the principles of mathematics, is there any contradictions left in these statements after rounding off? One person can not die in all of these years, obviously.

Thanks.

Answer
The sister's statement is wrong. Taking the average of the 3 answers does give 72.67, which when rounded to the nearest integer, is 73. However, this is not the same thing as saying this calculated answer is the same as the individual answers, and that they are therefore "correct" (even though one happened to be). If the rounded average was incorrect, because some of the answers were way off, then the sister would not have  been able to make her statement.

I don't know that there are any real contradictions here in a mathematical sense. A contradiction arises when an assumption is shown to be incorrect. If the sister had made the statement that any rounded average would give the correct answer, then a contradiction would be revealed if another relative had guessed a really wrong answer, say 22, in which case the rounded average would not equal 73. The sister's statement would then be incorrect and , in fact, a contradiction of her underlying assumption.

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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