Mathematicians: what's so special about evenness?
From Wikipedia:
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd. An integer is even if it is divisible by two and odd if it is not even.
Fine. But, is there anything more to it? I mean, 2 is the "only even prime number". That's like saying "2 is the only prime number divisible by two". Is that more remarkable than 3 being the only prime number divisible by three?
Even integer on number line is always followed by odd integer. But then again, integer divisible by 3 or 7 or n is always followed by nondivisible integer n1 times, so...
What I'm clumsily trying to say is: if we ignore cultural and historical references and capability of our brains to handle pattern of smallish numbers and sets, is "being even" meaning anything more than "being divisible by two" from purely mathematical standpoint?
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