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anonymous
 one year ago
Show an informal proof to show that the following conjecture is true
Conjecture: The sum of an odd number and an even number is an odd number
anonymous
 one year ago
Show an informal proof to show that the following conjecture is true Conjecture: The sum of an odd number and an even number is an odd number

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I mostly don't really know how to type a informal proof.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Think of the integers. ... , 3, 2, 1, 0, 1, 2, 3, ...

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Some integers are even, and some are odd. If you multiply every integer by 2, are the products odd or even?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Correct. ... , 2(3), 2(2), 2(1), 2(0), 2(1), 2(2), 2(3), ... are all even

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Since 2 times each integer is an even integer, we can write For every integer n, 2n is an even integer.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Then by the same token, we can write For every integer n, 2n + 1 is an odd integer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just really don't understand how to prove that. with an informal proof

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0We're getting there. So far do you understand that for every integer, n, 2n is an even integer, and for every integer n, 2n + 1 is an odd integer?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Now let's add the numbers. odd even What is (2n + 1) + (2n) ? (2n + 1) + (2n) = = 2n + 1 + 2n = 4n + 1 = 2(2n) + 1 Since for every integer n, 2n is an even integer, then 2(2n) must be even. Therefore, 2(2n) + 1 = 4n + 1 is odd.
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