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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

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  1. anonymous
    • one year ago
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    I mostly don't really know how to type a informal proof.

  2. mathstudent55
    • one year ago
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    Think of the integers. ... , -3, -2, -1, 0, 1, 2, 3, ...

  3. mathstudent55
    • one year ago
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    Some integers are even, and some are odd. If you multiply every integer by 2, are the products odd or even?

  4. anonymous
    • one year ago
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    even

  5. mathstudent55
    • one year ago
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    Correct. ... , 2(-3), 2(-2), 2(-1), 2(0), 2(1), 2(2), 2(3), ... are all even

  6. mathstudent55
    • one year ago
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    Since 2 times each integer is an even integer, we can write For every integer n, 2n is an even integer.

  7. mathstudent55
    • one year ago
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    Then by the same token, we can write For every integer n, 2n + 1 is an odd integer.

  8. anonymous
    • one year ago
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    I just really don't understand how to prove that. with an informal proof

  9. mathstudent55
    • one year ago
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    We'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?

  10. mathstudent55
    • one year ago
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    Now 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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