Text: Ταῦτα ἔγραψα ὑμῖν ἵνα εἰδῆτε ὅτι ζωὴν ἔχετε αἰώνιον, τοῖς πιστεύουσιν εἰς τὸ ὄνομα τοῦ Υἱοῦ τοῦ Θεοῦ. (1 John 5:13)
After using the epistolary aorist (ἔγραψα), John next employs the ἵνα or purpose clause. Therefore, his words might properly read: "I write you these things [in order] that . . ."
Next, we encounter εἰδῆτε. εἰδῆτε is a present subjunctive active form (not an infinitive which = to + the verb). Therefore, this verb should ideally not be rendered "to know," etc. It is more literally, "you might/may know" since it's also second person plural.
Furthermore, the additional utilization of the ὅτι clause and the preposition εἰς emphasize the point that the addresses of the letter "are having" (ἔχετε) eternal life.