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

*To*: mathgroup at smc.vnet.net*Subject*: [mg124277] How to check whether an infinite set is closed under addition?*From*: Rex <aoirex at gmail.com>*Date*: Sun, 15 Jan 2012 04:51:49 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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.

**Follow-Ups**:**Re: How to check whether an infinite set is closed under***From:*DrMajorBob <btreat1@austin.rr.com>