In the equation a=bq+r,
if b=2, then every can be written in the form 2q or 2q+1.
The numbers of the form 2q are all evens and
the numbers of the form 2q+1 are all odds.
Zero is of the form 2q. So it should be even.
Where is the confusion? Why is the confusion?
ZERO IS EVEN is obvious.
Harikrishna Holla G,
Brahmavara.
On Mon, Apr 25, 2016 at 2:28 PM, Harikrishna Holla <
harikrishnaho...@gmail.com> wrote:
> ಸೊನ್ನೆಯು ಒಂದು ಸಮ ಸಂಖ್ಯೆ ಎಂಬುದು ನಿರ್ವಿವಾದದ ಸಂಗತಿ. ಅದರ ಬಗ್ಗೆ ಸಂಶಯವೇ ಬೇಡ.
> ಸೊನ್ನೆಯು ಒಂದು ಸಮ ಸಂಖ್ಯೆಯೇ ಆಗಿದೆ.
>
>
> Harikrishna Holla G,
> Brahmavara.
>
> On Mon, Apr 25, 2016 at 2:27 PM, Harikrishna Holla <
> harikrishnaho...@gmail.com> wrote:
>
>> ಮ.ಸಾ.ಅ. ಮತ್ತು ಲ.ಸಾ.ಅ.ಗಳು ಧನ ಪೂರ್ಣಾಂಕಗಳಿಗೆ ಮಾತ್ರ ಸರಿಹೊಂದುತ್ತವೆ. ಆ ವಿಷಯ
>> ಇಲ್ಲಿ ಪ್ರಸ್ತಾಪಿಸಿದ್ದು ಯಾಕೋ ಗೊತ್ತಿಲ್ಲ.
>>
>>
>> Harikrishna Holla G,
>> Brahmavara.
>>
>> On Mon, Apr 25, 2016 at 2:25 PM, Harikrishna Holla <
>> harikrishnaho...@gmail.com> wrote:
>>
>>> Set of even numbers = {.......-6,-4,-2,0,2,4,6......}.
>>> Set of odd numbers = {.......-5,-3,-1,3,5......}.
>>> Negative integers can be even or odd.
>>> An integer (whether it is negative or nonnegative) should be either even
>>> or odd.
>>> No integer can be both even or odd. At the same time no integer can be
>>> neither even nor odd.
>>> "Euclid's division lemma a=bq+r can be extended to negative integers
>>> also" means in a=bq+r , a & q may be negative and 0 ≤ r < b.
>>> Eg: -6=2×(-3)+0 , -5=2×(-3)+1.......etc.
>>>
>>> Harikrishna Holla G,
>>> Brahmavara.
>>>
>>> On Mon, Apr 25, 2016 at 12:33 PM, Hanamanth Channal <channa...@gmail.com
>>> > wrote:
>>>
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>>>>
>>>> Except 0 we can define the numbers are either even or odd .
>>>>
>>>> Because it (0) devides both even and odd numbers perfectly i e
>>>> reminder is Zero.
>>>>
>>>> While considering even number system we can consider 0 too.
>>>> On 25 Apr 2016 11:58, "Ramesh H N" <rameshmysuru...@gmail.com> wrote:
>>>>
>>>>> Negative no.s are not even if u consider them as multiples of 2 then
>>>>> what is the least common multiple of 2 and 4.it is not possible to
>>>>> find if multiples of 2 is infinite set on negative side.so zero and
>>>>> negative multiples of 2 are not even
>>>>> On 24-Apr-2016 09:10, "Kumar B" <kumarb2261...@gmail.com> wrote:
>>>>>
>>>>> ...-4,-2,0,2,4,....these are even numbers. Bcoz this is sequence
>>>>> But zero have no sign (not plus or minus)
>>>>> .....,-3,-1,0,1,3,...these are not sequence, bcoz 3,1 are odd number,
>>>>> 0 is not odd
>>>>> On 24 Apr 2016 08:41, "Gireesha HP" <gireeshasushma2...@gmail.com>
>>>>> wrote:
>>>>>
>>>>>> PLEASE discuss about ....
>>>>>> Zero either..... Even or.... odd
>>>>>> Or neithr even nor odd....
>>>>>>
>>>>>> Confusions are still on ....
>>>>>>
>>>>>> --
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>>>>>> ಸಾರ್ವಜನಿಕ ಇಲಾಖೆಗೆ ಸಾರ್ವಜನಿಕ ತಂತ್ರಾಂಶ
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>>>>> --
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>>>>> 4. For doubts on Ubuntu, public software, visit
>>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Frequently_Asked_Questions
>>>>> 5. Are you using pirated software? Use Sarvajanika Tantramsha, see
>>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Why_public_software
>>>>> ಸಾರ್ವಜನಿಕ ಇಲಾಖೆಗೆ ಸಾರ್ವಜನಿಕ ತಂತ್ರಾಂಶ
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>>>>> --
>>>>> 1. If a teacher wants to join STF, visit
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>>>>> 2. For STF training, visit KOER -
>>>>> http://karnatakaeducation.org.in/KOER/en/index.php
>>>>> 4. For Ubuntu 14.04 installation, visit
>>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Kalpavriksha
>>>>> 4. For doubts on Ubuntu, public software, visit
>>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Frequently_Asked_Questions
>>>>> 5. Are you using pirated software? Use Sarvajanika Tantramsha, see
>>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Why_public_software
>>>>> ಸಾರ್ವಜನಿಕ ಇಲಾಖೆಗೆ ಸಾರ್ವಜನಿಕ ತಂತ್ರಾಂಶ
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>>>> --
>>>> 1. If a teacher wants to join STF, visit
>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Become_a_STF_groups_member
>>>> 2. For STF training, visit KOER -
>>>> http://karnatakaeducation.org.in/KOER/en/index.php
>>>> 4. For Ubuntu 14.04 installation, visit
>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Kalpavriksha
>>>> 4. For doubts on Ubuntu, public software, visit
>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Frequently_Asked_Questions
>>>> 5. Are you using pirated software? Use Sarvajanika Tantramsha, see
>>>> http://karnatakaeducation.org.in/KOER/en/index.php/Why_public_software
>>>> ಸಾರ್ವಜನಿಕ ಇಲಾಖೆಗೆ ಸಾರ್ವಜನಿಕ ತಂತ್ರಾಂಶ
>>>> ---
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>>>>
>>>>
>>>
>>
>
--
1. If a teacher wants to join STF, visit
http://karnatakaeducation.org.in/KOER/en/index.php/Become_a_STF_groups_member
2. For STF training, visit KOER -
http://karnatakaeducation.org.in/KOER/en/index.php
4. For Ubuntu 14.04 installation, visit
http://karnatakaeducation.org.in/KOER/en/index.php/Kalpavriksha
4. For doubts on Ubuntu, public software, visit
http://karnatakaeducation.org.in/KOER/en/index.php/Frequently_Asked_Questions
5. Are you using pirated software? Use Sarvajanika Tantramsha, see
http://karnatakaeducation.org.in/KOER/en/index.php/Why_public_software
ಸಾರ್ವಜನಿಕ ಇಲಾಖೆಗೆ ಸಾರ್ವಜನಿಕ ತಂತ್ರಾಂಶ
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