Adding an Even and an Odd Number
Date: 03/26/2003 at 19:21:39 From: Debbie Subject: Addition Can you think of any two numbers, one even and the other odd, whose sum is even? My son is in the third grade, and this was one of his homework questions. We have tried different combinations of even and odd numbers and can't come up with an even number answer.
Date: 03/27/2003 at 00:58:37 From: Doctor Ian Subject: Re: Addition Hi Debbie, It depends on how tricky you want to get. If you're just using standard arithmetic, you're right. No such pair of numbers exists: 19 Odd Number Puzzle http://mathforum.org/library/drmath/view/57207.html However, see: Can the Sum of 5 Odd Numbers Equal an Even Number? http://mathforum.org/library/drmath/view/61945.html Probably, though, the point of the exercise is to help your son get the idea that it's not enough to just try a bunch of examples. If you want to make a claim about _all_ numbers, then you have to construct more general explanations. For example, suppose I ask you this: I'm thinking of a number, say 3. I'm going to multiply it by itself: 3 * 3 = 9. And then I'll multiply it by itself twice: 3 * 3 * 3 = 27. Can you think of any number for which the second product will be less than the first? Now, you might try a bunch of examples: 3 * 3 < 3 * 3 * 3 5 * 5 < 5 * 5 * 5 21 * 21 < 21 * 21 * 21 and you might conclude, from these examples, that there is no number for which the second product is less than the first. But you'd be wrong: -1 * -1 > -1 * -1 * -1 Also, 1/2 * 1/2 > 1/2 * 1/2 * 1/2 So you can _never_ base a general statement about all numbers on a finite number of examples using particular numbers, because there is always a chance, no matter how small, that you have forgotten to look at the numbers that would prove you wrong. And understanding that is the first step towards understanding what proofs are, and how they work. Does that make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 04/02/2003 at 21:05:36 From: Debbie Subject: Thank you (Addition) Thank you. I love your site. It is very informative, and I use it very often when helping my son with his homework. Again, THANKS!
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