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 Zeration MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 03/23/2015, 02:31 PM (03/23/2015, 01:39 PM)marraco Wrote: (03/21/2015, 11:11 PM)tommy1729 Wrote: a*b = b*a "add+b"^[a-1](1*b) = "add+a"^[b-1](1*a)That would mean b*(a-1)=a*(b-1) but if "-" is an inverse operator of [q], such that x-y is defined as x-y=x[q]-y, and -y is defined as y[q]-y=N(q,y) then for [q]=product, "-" would be division, soUre misunderstanding the expression $f^{n}(x)$ In fact Tommy tryes to replace g and f with "add_b" and "add_1" and the interpretation becomes the following Quote:General case $f^{a - N_q}(N_q[q]b) = g^{b - N_q}(N_q[q]a)$ - Case q=1 with $[1]=+$, $f(x)=g(x)={\rm add}_1(x)=x+1$ and $N_1=0$ ${\rm add}_1^{a - N_1}(N_1[1]b) = {\rm add}_1^{b - N_1}(N_1[1]a)$ ${\rm add}_1^{a - 0}(0+b) = {\rm add}_1^{b -0}(0+a)$ ${\rm add}_1^{a }(b)=a+b =b+a= {\rm add}_1^{b }(a)$ - Case q=2 with $[2]=\cdot$, $f(x)={\rm add}_b(x)=b+x$, $g(x)={\rm add}_a(x)=a+x$ and $N_2=1$ ${\rm add}_b^{a - N_2}(N_1[2]b) = {\rm add}_a^{b - N_2}(N_2[2]a)$ ${\rm add}_b^{a - 1}(1 \cdot b) = {\rm add}_1^{b -1}(1\cdot a)$ $(b+...+b)_{a-1 times}+(b)=(a+...+a)_{b-1 times}+(a)$ $b(a-1)+(b)=a(b-1)+(a)$ $(ba-b)+(b)=ba=ab=(ab-a)+(a)$ - Case q=0 with $[0]=\circ$ and $N_0=-\infty$, but in this case how we get the following $f^{a -(-\infty)}((-\infty)[0]b) = g^{b - (-\infty)}((-\infty)[0]a)$ $f^{+\infty}(b) = g^{+\infty}(a)$ Quote:-∞ is used on all the basic operations: the neutral of addition is ÷∞=1/∞=0 the neutral of product is ∞√=∞√n=n^÷∞=1 the neutral of exponentiation is $^{-\infty}n=n^{\frac{1}{n}}$ from product viewpoint, all numbers smaller than 0 are transfinite. from exponentiation of n viewpoint, all numbers smaller than 1 are transfinite. from tetration of n viewpoint, all numbers smaller than $n^{\frac{1}{n}}$ are transfinite. Agree with this last point... It really deserves some attention imho. MathStackExchange account:MphLee « Next Oldest | Next Newest »

 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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