• EatBorekYouWreck@lemmy.world
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    1 year ago

    Even vs odd numbers are not as important as we think they are. We could do the same to any other prime number. 2 is the only even prime (meaning it is divisible by 2) 3 is the only number divisible by 3. 5 is the only prime divisible by 5. When you think about the definition of prime numbers, this is a trivial conclusion.

    Tldr: be mindful of your conventions.

    • alvvayson@lemmy.world
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      1 year ago

      Yes, but not really.

      With 2, the natural numbers divide into equal halves. One of which we call odd and the other even. And we use this property a lot in math.

      If you do it with 3, then one group is going to be a third and the other two thirds (ignore that both sets are infinite, you may assume a continuous finite subset of the natural numbers for this argument).

      And this imbalance only gets worse with bigger primes.

      So yes, 2 is special. It is the first and smallest prime and it is the number that primarily underlies concepts such as balance, symmetry, duplication and equality.

      • EatBorekYouWreck@lemmy.world
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        1 year ago

        But why would you divide the numbers to two sets? It is reasonable for when considering 2, but if you really want to generalize, for 3 you’d need to divide the numbers to three sets. One that divide by 3, one that has remainder of 1 and one that has remainder of 2. This way you have 3 symmetric sets of numbers and you can give them special names and find their special properties and assign importance to them. This can also be done for 5 with 5 symmetric sets, 7, 11, and any other prime number.