Then according to u what is the definition of even no. On 25-Apr-2016 14:30, "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 2:30 PM, Harikrishna Holla < > harikrishnaho...@gmail.com> wrote: > >> Yes , b is positive. >> >> Harikrishna Holla G, >> Brahmavara. >> >> On Mon, Apr 25, 2016 at 11:50 AM, Ramesh H N <rameshmysuru...@gmail.com> >> wrote: >> >>> Sir u r condition clearly indicating that 0 <r<b indicates that b is >>> possitive >>> On 25-Apr-2016 07:45, "Harikrishna Holla" <harikrishnaho...@gmail.com> >>> 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 <mnmah...@gmail.com> wrote: >>>> >>>>> [image: Boxbe] <https://www.boxbe.com/overview> This message is >>>>> eligible for Automatic Cleanup! (mnmah...@gmail.com) Add cleanup rule >>>>> <https://www.boxbe.com/popup?url=https%3A%2F%2Fwww.boxbe.com%2Fcleanup%3Ftoken%3D2D8XlGkK31uXRScULOs4oref3kT3LLcXTgrUPeaRoPeWfgsBpDM11xISp03sPazljtjYskdmtYu4SVeNeFK%252B%252B26q2RH6sm94hLJGRcvBJTiZkEN86k0r79gC409lLFb96kEy09y9SGY%253D%26key%3Dah%252FxOV%252Bjm1dBdUAIskwMbyspp4c1JQN%252FkIT8DwMrj6o%253D&tc_serial=25182272455&tc_rand=2024656766&utm_source=stf&utm_medium=email&utm_campaign=ANNO_CLEANUP_ADD&utm_content=001> >>>>> | More info >>>>> <http://blog.boxbe.com/general/boxbe-automatic-cleanup?tc_serial=25182272455&tc_rand=2024656766&utm_source=stf&utm_medium=email&utm_campaign=ANNO_CLEANUP_ADD&utm_content=001> >>>>> >>>>> Reference introduction of maths .. >>>>> On Apr 24, 2016 8:43 PM, "Harikrishna Holla" < >>>>> harikrishnaho...@gmail.com> 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. >>>>>> >>>>>> -- >>>>>> 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 >>>>>> --- >>>>>> You received this message because you are subscribed to the Google >>>>>> Groups "Maths & Science STF" group. >>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>> send an email to mathssciencestf+unsubscr...@googlegroups.com. >>>>>> To post to this group, send email to mathssciencestf@googlegroups.com >>>>>> . >>>>>> Visit this group at https://groups.google.com/group/mathssciencestf. >>>>>> For more options, visit https://groups.google.com/d/optout. >>>>>> >>>>> -- >>>>> 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 >>>>> --- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "Maths & Science STF" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to mathssciencestf+unsubscr...@googlegroups.com. >>>>> To post to this group, send email to mathssciencestf@googlegroups.com. >>>>> Visit this group at https://groups.google.com/group/mathssciencestf. >>>>> For more options, visit https://groups.google.com/d/optout. >>>>> >>>>> >>>> -- >>>> 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 >>>> --- >>>> You received this message because you are subscribed to the Google >>>> Groups "Maths & Science STF" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to mathssciencestf+unsubscr...@googlegroups.com. >>>> To post to this group, send email to mathssciencestf@googlegroups.com. >>>> Visit this group at https://groups.google.com/group/mathssciencestf. >>>> For more options, visit https://groups.google.com/d/optout. >>>> >>> -- >>> 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 >>> --- >>> You received this message because you are subscribed to the Google >>> Groups "Maths & Science STF" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to mathssciencestf+unsubscr...@googlegroups.com. >>> To post to this group, send email to mathssciencestf@googlegroups.com. >>> Visit this group at https://groups.google.com/group/mathssciencestf. >>> For more options, visit https://groups.google.com/d/optout. >>> >> >> > -- > 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 > --- > You received this message because you are subscribed to the Google Groups > "Maths & Science STF" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to mathssciencestf+unsubscr...@googlegroups.com. > To post to this group, send email to mathssciencestf@googlegroups.com. > Visit this group at https://groups.google.com/group/mathssciencestf. > For more options, visit https://groups.google.com/d/optout. > -- 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 --- You received this message because you are subscribed to the Google Groups "Maths & Science STF" group. To unsubscribe from this group and stop receiving emails from it, send an email to mathssciencestf+unsubscr...@googlegroups.com. To post to this group, send an email to mathssciencestf@googlegroups.com. Visit this group at https://groups.google.com/group/mathssciencestf. 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