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.
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.
Not sure about how relevant this in reality, but when it comes to alternating series, this might be relevant.
For example the Fourier series expansion of cosine and other trig function?
True, but normally, you’d introduce trig functions before complex numbers.
Anyhow: I appreciate the meme and the complete over the top discussion about it :D
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.
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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.
Not sure about how relevant this in reality, but when it comes to alternating series, this might be relevant. For example the Fourier series expansion of cosine and other trig function?
But then it is more natural to use the complex version of the Fourier series, which has a neat symmetric notation
True, but normally, you’d introduce trig functions before complex numbers. Anyhow: I appreciate the meme and the complete over the top discussion about it :D
Complex numbers ftw
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You’d have one set that are multiples of 3, one set that are multiples of 3 plus 1, and one stat that are multiples of 3 minus 1 (or plus 2)
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I don’t know if it’s intentional or not, but you’re describing cyclical groups
Not intentionally, but yes group rise in many places unexpectedly. That’s why they’re so neat