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This is a follow-up question.


Thanks for your answer. I am sorry for my wrong question. What I meant was "5+5 isn't equal to 9"

You are right. But don't you think that rounding off doesn't really give a correct answer. If I say that 9 is the closest number to 10, that doesn't make 5+5=9. Don't you think that sister is COMPLETELY inaccurate when she tries to reconcile these ages? What do you say? For example, if a person dies and there is a controversy about the age at which he died, and all the above ages (70. 73, 75) are given, then is it possible to find the age at which the person died or to reconcile between them? A person can never die at all these ages.

Thanks.

Answer
No worries.

I think the trouble you're having is trying to deduce the true, absolutely accurate answer from mere estimates (guesses). It really can't be done, at least with a finite number of estimates. You'll have to be content with having an answer with a certain amount of error.I think you're interpreting this error with a "contradiction". Perhaps a better concept would be consistency. In other words, an estimated answer that is a non-integer, like 72.67, which is close to but not exactly equal to an integer, is inconsistent with the requirement that it be an integer, i.e., 73.

In the same line of reasoning, having different people give different values (guesses) for a person's age is already inconsistent with the axiom that a person can die at only one age.

BTW, your logic statement about 9 and 10 needs to be tightened up a bit. The statement that 9 is close to 10 can be written

9 ≈ 10

using the approximately equal sign, ≈. Then it is OK to write

5 + 5 ≈ 9

which does not imply 5 + 5 = 9.

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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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