Re: How to check whether an infinite set is closed under addition?

*To*: mathgroup at smc.vnet.net*Subject*: [mg124302] Re: How to check whether an infinite set is closed under addition?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Mon, 16 Jan 2012 17:10:32 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 15 Jan 2012, at 10:51, Rex wrote: > Given k positive numbers a_1<a_2<a_3<...<a_k, and all integers greater > than a_k, we want to check whether this set {a_1, a_2, a_3,...a_k, a_k > + 1, a_k+2, ......} is closed under addition. > > Is there any easy way to do this? any functions that we could use in > Mathematica? > > Your help will be greatly appreciated. > > Let's call your set {a1,a2,...,a3} "base". Then: closedQ[base_List] := Complement[Select[Total[Subsets[base, {2}], {2}], # <= Max[base] &], base] == {} For example: closedQ[{1, 2, 3}] True closedQ[{1, 4, 6, 7}] False Andrzej Kozlowski