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John's final epistle is addressed to Gaius, probably a leading member of a local church and one of John's own converts, as he referred to Gaius as his own child (1:4). Just as in his second letter, John mentions the treatment of itinerant teachers, only this time in reference to true Christian missionaries as opposed to false teachers. Christians ought to show hospitality to the former group while shunning the latter group.
A first-century church manual known as the Didache indicates that early Christian hospitality was sometimes abused. It stated that anyone claiming to be an apostle who stayed longer than two days or who asked for money was a false apostle! True prophets had a right to stay and be supported, but ordinary Christian travelers were not to be entertained for free for more than two or three days. Those who wanted to settle for longer periods should work to support themselves, otherwise they were "trading on Christ."
John commended Gaius for his hospitality towards traveling ministers, stating that we ought to be involved in supporting such men that we may be "fellow workers with the truth" (1:8). Not all of us can take the gospel to foreign places, but all of us can help those who can. (You can support your own national missionary, by the way, through Heaven's Family's National Missionary program!)
Contrasted with Gaius is a man by the name of Diotrephes who obviously held considerable influence in the church. He was marked by John as a self-seeking slanderer who had not "received the brethren" as Gaius had, and he even excommunicated those who did receive them. John would publicly expose Diotrephes when he arrived (1:10). Sometimes, in the interests of the entire church, hypocrisy must be exposed. This is particularly true when the sinning individual is in a position of leadership in the church. Covering such a person's sins under the guise of "walking in love" is not walking in love toward the people he leads and influences.
Verse 2 of this short letter is often used by prosperity preachers to prove to their greedy audiences that God wants them to become even wealthier than they already are. In light of what we recently read in John's first epistle, however, it would be incredibly foolish for us to conclude that John hoped Gaius would become rich so he could live in luxury and self-indulgence. The only reason John wanted Gaius to prosper would be so he would have more to share. Gaius was a loving servant of the brethren, a financial supporter of traveling missionaries (1:5-8), and if he prospered (and enjoyed good health, John's other desire) he could serve and give all the more.
All of this being so, certainly it should be our desire that every Christian who is seeking first God's kingdom will prosper, because more good would be done by their obedience to Christ and their love for the brethren. 100% of their prosperity can be used to do more good. But to teach that 3 John 2 proves that God wants those of us who are already so wealthy by the world's standard to increase our luxury and self-indulgence---as exemplified by modern prosperity preachers---is entirely unwarranted.