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 2:30 PM, Harikrishna Holla <
[email protected]> wrote:
> Yes , b is positive.
>
> Harikrishna Holla G,
> Brahmavara.
>
> On Mon, Apr 25, 2016 at 11:50 AM, Ramesh H N <[email protected]>
> wrote:
>
>> Sir u r condition clearly indicating that 0 <r<b indicates that b is
>> possitive
>> On 25-Apr-2016 07:45, "Harikrishna Holla" <[email protected]>
>> wrote:
>>
>>> No sir, Euclid's Lemma can be extended to negative integers also. Only
>>> condition is 0 ≤ r < b.
>>>
>>>
>>> Harikrishna Holla G,
>>> Brahmavara.
>>>
>>> On Sun, Apr 24, 2016 at 9:15 PM, mahi mn <[email protected]> wrote:
>>>
>>>> [image: Boxbe] <https://www.boxbe.com/overview> This message is
>>>> eligible for Automatic Cleanup! ([email protected]) Add cleanup rule
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>>>>
>>>> Reference introduction of maths ..
>>>> On Apr 24, 2016 8:43 PM, "Harikrishna Holla" <
>>>> [email protected]> wrote:
>>>>
>>>>> 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.
>>>>>
>>>>> --
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>>>> 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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>>
>
>
--
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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