Zeration

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Zeration

marraco $Offline$
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Posts: 100
Threads: 12
Joined: Apr 2011

#72

03/24/2015, 11:29 AM

(03/21/2015, 11:11 PM)tommy1729 Wrote: f and g are some function :

f^[a - N_q](N_q[q]b) = g^[b - N_q](N_q[q]a)

(03/23/2015, 02:31 PM)MphLee Wrote:
Quote:General case $f^{a - N_q}(N_q[q]b) = g^{b - N_q}(N_q[q]a)$

maybe this one is clearer?
$f^{a}(N_{(q,a)}) = g^{b}(N_{(q,b)})$
$f(x)=x {\small{[q-1]}} b$
$g(x)=x {\small{[q-1]}} a$

I added a subindex to the neutral, because many operations have a different neutral for each number.

For example, right bracket tetration:
$(..((a_1)^{a_2})^{a_3}^ \,...)^{a_b}=a^{a^{b-1}}$ , where
$f_{(x)}=x {\small{[3]}} b = x^b$
$g_{(x)}=x {\small{[3]}} a = x^a$

...looks non intuitive. Unnecessarily complicated.
But each "a" has a neutral $N_{()4,a}\,=\, a^{a^{-1}}$ , which simplifies the notation:

$(..((({N_a)}^{a_1})^{a_2})^{a_3}^ \,...)^{a_b}={N_a\,}^{a^{a^b}}$

(03/21/2015, 11:11 PM)tommy1729 Wrote: f^[a - oo](...) does not make sense as a nonconstant function.

a+b = b+a

"add+1"^[a](0) = "add+1"^[b ](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

Zeration - My Research / Investigation - by James Knight - 03/25/2008, 08:28 AM

RE: Zeration - My Research / Investigation - by bo198214 - 03/25/2008, 09:09 AM

More on Zeration - by James Knight - 03/25/2008, 03:44 PM

Exponential Laws - New Zeration Law - by James Knight - 03/25/2008, 07:48 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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