• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Non-trivial extension of max(n,1)-1 to the reals and its iteration. MphLee Fellow Posts: 184 Threads: 19 Joined: May 2013 05/16/2014, 01:37 PM (This post was last modified: 05/16/2014, 02:40 PM by MphLee.) I was very interested in the problem of extending $max(n,1)-1$ to the reals (that is actual the "incomplete" predecessor function $S^{\circ (-1)}$ over the naturals) I've asked the same question on MSE but it was a bit ignored...I hope because it is trivial! http://math.stackexchange.com/questions/...its-fracti The question is about extensions of $A(n):=max(n,1)-1$ to the reals with some conditions Quote:A-$A(x)=max(x,1)-1$ only if $x \in \mathbb{N}$ B-$A(x)$ is not discontinuous I just noticed that I've made a lot of errors in my MathSE question, I'll fix it in this post (and later on mathSE) From successor and inverse successor we can define the subtraction in this way $x-0:=x$ and $x-(y+1):=S^{\circ(-1)}(x-y)$ with $A$ , that is a modified predecessor function we could define its iteration using an "esotic subtraction" that is "incomplete" for naturals and is "complete" for reals (like we are cutting all the negative integers) Quote:$x -^* 0:=x$ $x-^* (n+1)=A(x-^* n)$ In this way we have Quote:$x-^*1=A(x)$ and $x-^*n=A^{\circ n}(x)$ How we can go in order to extend $x-^*y$ to real $y$? For example what can we know about $x-0,5$ ? for example $(x-^*0.5)-^*1=(x-^*1)-^*0.5=x-^*1.5$ if we put $x=0$ $(0-^*0.5)-^*1=(0-^*1)-^*0.5=0-^*1.5$ then if $0_^*0.5=\alpha$ $\alpha-^*1=0-^*0.5=0-^*1.5$ if $\alpha$ is not a natural number $\alpha-^*1=\alpha=0-^*1.5$ !?? what is going on here? If $\alpha$ is natural $max(\alpha,1)-1=\alpha=0-^*1.5$ in this case we should have that $\alpha=0$. What do you think about this? MathStackExchange account:MphLee Fundamental Law $(\sigma+1)0=\sigma (\sigma+1)$ « Next Oldest | Next Newest »

 Messages In This Thread Non-trivial extension of max(n,1)-1 to the reals and its iteration. - by MphLee - 05/16/2014, 01:37 PM RE: Non-trivial extension of max(n,1)-1 to the reals and its iteration. - by tommy1729 - 05/16/2014, 09:21 PM RE: Non-trivial extension of max(n,1)-1 to the reals and its iteration. - by MphLee - 05/16/2014, 10:20 PM RE: Non-trivial extension of max(n,1)-1 to the reals and its iteration. - by MphLee - 05/17/2014, 07:10 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Ueda - Extension of tetration to real and complex heights MphLee 2 92 12/03/2021, 01:23 AM Last Post: JmsNxn On extension to "other" iteration roots Leo.W 7 881 09/29/2021, 04:12 PM Last Post: Leo.W Possible continuous extension of tetration to the reals Dasedes 0 2,764 10/10/2016, 04:57 AM Last Post: Dasedes Andrew Robbins' Tetration Extension bo198214 32 70,478 08/22/2016, 04:19 PM Last Post: Gottfried Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 5,156 06/15/2013, 08:02 PM Last Post: MphLee extension of the Ackermann function to operators less than addition JmsNxn 2 6,740 11/06/2011, 08:06 PM Last Post: JmsNxn Iteration series: Different fixpoints and iteration series (of an example polynomial) Gottfried 0 4,495 09/04/2011, 05:59 AM Last Post: Gottfried Fractional iteration of x^2+1 at infinity and fractional iteration of exp bo198214 10 26,370 06/09/2011, 05:56 AM Last Post: bo198214 Tetration Extension to Real Heights chobe 3 9,773 05/15/2010, 01:39 AM Last Post: bo198214 Tetration extension for bases between 1 and eta dantheman163 16 31,436 12/19/2009, 10:55 AM Last Post: bo198214

Users browsing this thread: 1 Guest(s)