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Zeration
#11
andydude Wrote:If we choose to hold to be true for all N, then the natural consequence is that for all a ... .
If we choose to hold true for all N, then we get for a == b. Both cannot be true, so we must make a choice.

Hm, the first one (demanding that a[N-1](a[N]b)=a[N](b+1) for all real b and integer N) seems to be the pure approach.
Interestingly the derivation of a previous operation seems not to depend on an intial condition like a[N]1=a (which is not true for N=1, but for all N>1).

But we just could conclude from a[N-1](a[N]b)=a[N](b+1) that a[0]b=b+1. And we can further conclude from
a[-1](a[0]b)=a[0](b+1)
that
a[-1](b+1)=a[0](b+1)
hence
a[-1]b=a[0]b=b+1 moreover by induction that a[N]b=b+1 for all N<0.
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Messages In This Thread
Zeration - by GFR - 02/14/2008, 06:38 PM
RE: Zeration - by Ivars - 02/14/2008, 08:10 PM
RE: Zeration - by GFR - 02/14/2008, 10:41 PM
RE: Zeration - by mathamateur - 07/30/2009, 06:31 AM
RE: Zeration - by Ivars - 02/21/2008, 07:22 PM
RE: Zeration - by quickfur - 02/21/2008, 09:34 PM
RE: Zeration - by bo198214 - 02/21/2008, 10:18 PM
RE: Zeration - by bo198214 - 02/21/2008, 10:25 PM
RE: Zeration - by quickfur - 02/21/2008, 11:04 PM
RE: Zeration - by quickfur - 02/21/2008, 11:12 PM
RE: Zeration - by KAR - 02/21/2008, 11:04 PM
RE: Zeration - by quickfur - 02/21/2008, 11:52 PM
RE: Zeration - by GFR - 02/24/2008, 12:39 AM
RE: Zeration - by Ivars - 02/24/2008, 02:50 PM
RE: Zeration - by marraco - 03/20/2015, 09:59 PM
RE: Zeration - by bo198214 - 02/24/2008, 11:02 AM
RE: Zeration - by GFR - 03/19/2008, 12:40 PM
More on Zeration - by James Knight - 03/25/2008, 03:44 PM
Delta Numbers As HyperReals - by James Knight - 03/26/2008, 12:50 AM
RE: Delta Numbers As HyperReals - by Ivars - 03/26/2008, 12:15 PM
RE: Zeration - by GFR - 03/26/2008, 12:22 AM
RE: Zeration - by GFR - 04/05/2008, 08:58 PM
RE: Zeration - by Igor M - 01/14/2009, 04:04 PM
RE: Zeration - by bo198214 - 01/20/2009, 09:59 PM
RE: Zeration - by 73939 - 07/05/2010, 12:00 AM
RE: Zeration - by bo198214 - 07/05/2010, 07:37 AM
RE: Zeration - by brangelito - 07/20/2010, 05:51 PM
RE: Zeration - by bo198214 - 07/21/2010, 02:58 AM
RE: Zeration - by JmsNxn - 11/09/2011, 01:40 AM
RE: Zeration - by quickfur - 11/09/2011, 04:15 AM
RE: Zeration - by JmsNxn - 11/10/2011, 01:20 AM
RE: Zeration - by quickfur - 11/10/2011, 02:09 AM
RE: Zeration - by marraco - 03/20/2015, 09:44 AM
RE: Zeration - by marraco - 03/20/2015, 10:41 PM
RE: Zeration - by marraco - 03/21/2015, 12:35 AM
RE: Zeration - by marraco - 03/21/2015, 01:44 AM
RE: Zeration - by marraco - 03/21/2015, 04:10 AM
RE: Zeration - by MphLee - 03/21/2015, 11:53 AM
RE: Zeration - by marraco - 03/23/2015, 07:58 AM
RE: Zeration - by tommy1729 - 03/21/2015, 11:11 PM
RE: Zeration - by marraco - 03/23/2015, 08:05 AM
RE: Zeration - by marraco - 03/24/2015, 11:29 AM
RE: Zeration - by MphLee - 03/23/2015, 09:00 AM
RE: Zeration - by marraco - 03/23/2015, 01:39 PM
RE: Zeration - by MphLee - 03/23/2015, 02:31 PM
RE: Zeration - by Stanislav - 05/28/2015, 11:12 PM
RE: Zeration - by marraco - 05/29/2015, 01:33 AM
RE: Zeration - by Stanislav - 05/29/2015, 09:06 PM
RE: Zeration - by MphLee - 06/03/2015, 01:40 PM
RE: Zeration - by Stanislav - 06/04/2015, 06:44 AM
RE: Zeration - by marraco - 06/04/2015, 08:44 PM
RE: Zeration - by MphLee - 06/05/2015, 09:10 PM
RE: Zeration - by Stanislav - 09/09/2015, 10:04 PM
RE: Zeration - by Stanislav - 10/31/2016, 02:57 PM

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