Is one wrong answer more wrong?

[surftheiop]

and engineering or any real world application of math for that matter

[AlexM]

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If I say "2 + 2 = 5", and someone else says "2 + 2 = -63", is it correct to say that he is 'more wrong'.

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I would say yes. Obviously in this situation both answers just look stupid, but if we were dealing with numbers in the trillions and someone was one off with more complicated equations than simple addition, it would be hard to say that the person who is 1 off isn't "less wrong" than the person who is trillions off.

[Borodog]

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If I say "2 + 2 = 5"

[/ QUOTE ]

Are you an astrophysicist?

Close enough.

[madnak]

[ QUOTE ]
sure one is more wrong.

if a cashier overcharges you a dollar, and your buddy 2 dollars,

did one of you get overcharged more?

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He gets overcharged more, but that doesn't mean the cashier was "more wrong" in his case. In fact, he may have been "less wrong" by some standards. What if your true total is $.75, while your buddy's total is $214.99?

Another example. Imagine that I'm measuring the distance to a certain star, and so is my friend. I like the number 50, so I guess "50 parsecs." My friend works out some calculations, and they're almost perfect - but he makes a careless mistake and comes up with 70 parsecs as his answer. The actual distance of the star is 45 parsecs. Am I more right?

And what if my answer to 2+2 is 8? Or 40? Maybe -4? At least these are all divisible by 2, and have a meaningful relationship to the correct answer of 4. Can we say that 5 is "more correct" because it happens to be in closer proximity to the correct answer? What if having an even number, or a number with the digit "4" in it, is important to our application?

[andyfox]

Depends. If someone tells us to go up two floors from the second floor to pick up our checks and I end up on floor 5 and you end up on floor -63, you're going to have a harder time getting to the right place than I. But if we're taking a math test, we both get the problem wrong.

[Borodog]

4 ~ 5

4 !~ -63

QED

[mickeyg13]

[ QUOTE ]
4 ~ 5

4 !~ -63

QED

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It depends on how you define the "~" operator. In some applications it might make sense to say that 5 is more right than 4, but if you want to speak strictly about mathematics, both answers are equally wrong. In a mathematics course, if the correct answer is pi, for instance, and a student writes 3.141592653 for an answer, then that answer is wrong, although that answer is more than fine for almost any conceivable engineering application.

[PLOlover]

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4 ~ 5

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4 is equal to 5 for extremely large values of 4. lol

[Phil153]

[ QUOTE ]
If I say "2 + 2 = 5", and someone else says "2 + 2 = -63", is it correct to say that he is 'more wrong'.

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The second is more wrong as it violates a greater number of basic principles. There are number of principles broadly and instinctively understood, such as proximity, relative size, oddness and evenness, positives making a positive, and so on. The first only violates a couple whereas the second violates several more, indicating that the person giving the second answer is more prone to error.

[stinkypete]

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[ QUOTE ]
4 ~ 5

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4 is equal to 5 for extremely large values of 4. lol

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i was thinking more along the lines of "4 has the same distribution as 5"