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Is 0 Even?

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  • E
    energizeddog M0★ M1 M2 M3★ M4 M5
    last edited by Sep 21, 2021, 2:27 PM

    "Two distinct even positive integers sum to 8. Determine the larger of these two integers."
    This question is from Module 0 Week 1 Challenge. The correct answer is 6 but I wrote 8. I googled it but they say zero is even. Is zero really even??

    M Q 2 Replies Last reply Sep 21, 2021, 11:38 PM Reply Quote 1
    • M
      modestwallaby M2★ M3★ M4★ M5 @energizeddog
      last edited by Sep 21, 2021, 11:38 PM

      @energizeddog 0 is not a positive integer

      1 Reply Last reply Reply Quote 1
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        Legendaryboy991 M0
        last edited by Sep 23, 2021, 10:12 PM

        I think 0 is even think. Here are the odd an even to 10. odd: 1, 3, 5, 7, 9. There are 5 odds. even: 2, 4, 6, 8. only 4. Plus zero would be 5.

        1 Reply Last reply Reply Quote 0
        • W
          wisemacaw M1
          last edited by Oct 4, 2021, 5:10 AM

          The parity of zero: The easiest way to prove that 0 is an even number:Check whether 0 meets the definition of an even number: if a number is an integer multiple of 2, then it is an even number. Since 0=0×2, 0 is an even number. In addition, 0 also satisfies all the properties of even numbers 0 is divisible by 2; the two integers adjacent to 0 are all odd numbers; 0 can be divided into two equal parts. 0 also satisfies some other models constructed from even numbers, such as some parity rules in arithmetic operations: even number-even number = even number. .

          TO BE CONTINUED...

          1 Reply Last reply Reply Quote 0
          • Q
            quacker88 MOD @energizeddog
            last edited by Oct 5, 2021, 1:19 AM

            @energizeddog Yup, it might seem weird to think about, but everything that @Legendaryboy991, @wisemacaw , and @modestwallaby are correct. 0 is an even number because it divides evenly into 2. \(\frac02=0\), which is a whole number, so 0 is even! All odd numbers are odd because they don't divide evenly into 2.

            So, although 0 is even, the pair that the question is looking for is still 2 and 6 since 0 is not positive. 0 is neither positive nor negative! A lot of problems will include words like "positive" and "nonnegative", so be careful when reading the questions in the future 🙂

            Note: can you tell me what the difference between "positive" and "nonnegative" is?

            E 1 Reply Last reply Oct 5, 2021, 3:40 AM Reply Quote 0
            • E
              energizeddog M0★ M1 M2 M3★ M4 M5 @quacker88
              last edited by Oct 5, 2021, 3:40 AM

              @quacker88 So if zero is neither positive nor negative, nonnegative means that a number is not negative, but 0 is not negative too! That means that nonnegative is all of the positive numbers PLUS zero itself, and positive just means all of the positive numbers but it does NOT include zero itself. So is all of that correct?

              Q 1 Reply Last reply Oct 28, 2021, 12:05 AM Reply Quote 0
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                Legendaryboy991 M0
                last edited by Oct 5, 2021, 10:52 PM

                The number zero is neither positive nor negative. Positive and negative numbers are sometimes called signed numbers.

                1 Reply Last reply Reply Quote 0
                • Q
                  quacker88 MOD @energizeddog
                  last edited by Oct 28, 2021, 12:05 AM

                  @energizeddog Sorry for replying so late-- but yes, perfect! That's exactly the difference. Way to go 😄

                  1 Reply Last reply Reply Quote 0

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