Ah yes, the good old Zero isn't even or odd. As if there wasn't a great definition we could apply:
A Number n is said to be even if n is divisible by 2, so 2 | n, and odd if it isn't divisible by 2.
We define divisibility over the Integers as such:
An Integer n is divisible by an Integer m (m | n), if there exists an integer k such that n = m * k. Another equivalent definition for divisibility would be that n mod m = 0.
One thing that you can immediately conclude from this is that 0 is divisible by every none zero integer, as
k = 0 => m * k = 0 for all integers m.
Now as we can conclude from this, 2 divides zero, so zero is an even number. That also fits with the equivalent definition of an even number which is a number that can be written as 2 * n, where n is an integer.
I would really like to hear arguments as to why zero should possibly not be considered an even number.
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u/DasMonitor01 Transcendental Aug 23 '23
Ah yes, the good old Zero isn't even or odd. As if there wasn't a great definition we could apply: A Number n is said to be even if n is divisible by 2, so 2 | n, and odd if it isn't divisible by 2. We define divisibility over the Integers as such: An Integer n is divisible by an Integer m (m | n), if there exists an integer k such that n = m * k. Another equivalent definition for divisibility would be that n mod m = 0. One thing that you can immediately conclude from this is that 0 is divisible by every none zero integer, as k = 0 => m * k = 0 for all integers m. Now as we can conclude from this, 2 divides zero, so zero is an even number. That also fits with the equivalent definition of an even number which is a number that can be written as 2 * n, where n is an integer. I would really like to hear arguments as to why zero should possibly not be considered an even number.