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#12 | |
"Robert Gerbicz"
Oct 2005
Hungary
112×13 Posts |
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The union of odd and even integers gives the integers, following your logic then the "quantity" of all integers is even, because that is the (disjoint) union set of two equal size set. But you already "proved" that it should be odd. Where is the cheat? |
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#13 |
Feb 2017
Nowhere
22×31×47 Posts |
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#14 |
Aug 2020
Guarujá - Brasil
2E16 Posts |
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If we were to list all the divisors of the number 0, we would need to list infinitely many numbers.
Since for every non-zero number we have its positive and negative number, then 0 has an "even infinite number" of non-zero divisors. The "infinite quantity is even" because for every non-zero number there is always the positive and the negative number in pairs. Both positive and negative numbers are divisors of 0. Although the division 0/0 is of indefinite value, whatever the finite number result is, the remainder will always be 0. If the division 0/0 produces an infinite number, also the remainder will still be 0. This is because we cannot add any remainder other than 0 to a finite or infinite product to get back the number 0. Because of the remainder 0, we may consider that 0 is a divisor of 0 itself with an undefined result. Because it is not possible to have a negative zero different from a positive zero, then 0 will always have an "odd infinite number" of divisors. Just as the other squares have an odd finite number of divisors, 0 has an "odd infinite number" of divisors. Last fiddled with by Charles Kusniec on 2022-02-10 at 14:02 |
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#15 |
Aug 2020
Guarujá - Brasil
2E16 Posts |
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Dear Administrator, if it is possible, please join with https://www.mersenneforum.org/showthread.php?t=27545 . Thank you,
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#16 |
Sep 2002
Database er0rr
2·11·191 Posts |
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#17 |
"Vincent"
Apr 2010
Over the rainbow
5×569 Posts |
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the odds of it being even or odd are even.
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#18 |
Feb 2017
Nowhere
22·31·47 Posts |
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