Please don't think I'm exaggerating when I say that John 20:31 is one of the most important passages in the scriptures. And it's in the text for this time. It's also a verse that essentially a book could be written about. (I recently heard the comment that "lots of ink has been spilled" over something, and, within that context, I actually thought that it was a cute picture to visualize, but there is no way I would use it here; this verse is much too important. All the ink--or toner--used would be worth it.)
I will give the verse to you here in a somewhat literal fashion, but hopefully you are already somewhat familiar with it: "...these things have been written in order that you may believe that Jesus is the Christ, the Son of God, and in order that, believing, you may have life in his name." There is, literally, so much here.
Where to begin? How about with one of the smallest words, "you"? The writer didn't say "lot's of people"; he used a direct pronoun. In a way, he is talking to the person who is reading or listening to the text.
But, also, in a way, he isn't. The form of "you" here is plural. In a way--in a very different way--he is saying, "y'all". He is talking to a group.
And that is a good reminder that this book doesn't promote a "me and Jesus" relationship. If you are by yourself, the devil can attack in lots of different ways, and he can certainly use your old sinful nature as his "trusty assistant". This verse sounds like it was meant to be read among a group.
And another issue is whether or not there is a "sigma"--the Greek letter "s"--in the phrase (actually it's just one word in Greek) "you may believe". With the letter, it sounds as if this account was addressed to non-Christians so that they might come to believe. Without the letter, it sounds as if this account was addressed to Christians so that their faith might be strengthened. That's certainly a lot of pressure on one letter! And there are old manuscripts both with and without this letter.
If you noticed, the way I translated it above was somewhat vague, "that you may believe...." I didn't want to confuse things there, but here I will state that I think it should be translated, "that you may continue to believe..."
The gospel accounts were written for use in the synagogues among the earliest Christians. They were treated with great reverence, much in the same way as the Old Testament was treated. The earliest Christians didn't have the money to give out gospel accounts like tracts. Paper was extremely expensive. And, as I have said before, they crafted these accounts very carefully. They wanted to make sure that they focused on Jesus.
I also wanted to say that I think we so easily pass by the part at the end, that we have life in his name. Notice that the pressure isn't on us to do something. We receive something here that is very special. The disciples showed us, in many and various ways, how what they did didn't amount to very much.
Ending on a positive (godly) note, is a much better thing. There's another chapter in this account, but I will save that for another time--and, by the way, it also focuses on Jesus.