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I am commenting page /info/en/?search=Parity_of_zero
If zero would be even, then we would say the following.
1. snakes have zero legs, if zero would be even,
we would say: snakes have an even number of legs.
2. pigs have zero wings, if zero would be even,
we would say: pigs have an even number of wings.
Zero 0 objects divided in groups of b > 0 objects,
will count 0 complete groups of b objects and 0 objects leftover,
that means 0/b = (q, r) = (0, 0) for any b > 0.
Even integers are named even, because divided in groups of 2,
will count at least one group of 2, but not less, having no leftover.
Considering "0 is even",
suggesting that 0 will count at least one group of 2,
that is false.
Generalization:
For a >= 0 and b >= 0, where a/b = (q, r) => b * q + r = a
a is incomplete aggregation, if q >= 0 and r > 0
a is complete aggregation, if q > 0 and r = 0
a = 0 is neutral aggregation, if q = 0 and r = 0
109.185.67.40 (
talk) 10:31, 21 February 2024 (UTC)
Mathematics desk | ||
---|---|---|
< February 20 | << Jan | February | Mar >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
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The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I am commenting page /info/en/?search=Parity_of_zero
If zero would be even, then we would say the following.
1. snakes have zero legs, if zero would be even,
we would say: snakes have an even number of legs.
2. pigs have zero wings, if zero would be even,
we would say: pigs have an even number of wings.
Zero 0 objects divided in groups of b > 0 objects,
will count 0 complete groups of b objects and 0 objects leftover,
that means 0/b = (q, r) = (0, 0) for any b > 0.
Even integers are named even, because divided in groups of 2,
will count at least one group of 2, but not less, having no leftover.
Considering "0 is even",
suggesting that 0 will count at least one group of 2,
that is false.
Generalization:
For a >= 0 and b >= 0, where a/b = (q, r) => b * q + r = a
a is incomplete aggregation, if q >= 0 and r > 0
a is complete aggregation, if q > 0 and r = 0
a = 0 is neutral aggregation, if q = 0 and r = 0
109.185.67.40 (
talk) 10:31, 21 February 2024 (UTC)