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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
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