{I have written} (egrapsa). Not epistolary aorist, but
refers to verses  1-12  of this Epistle as in  2:26  to the
preceding verses. {That ye may know} (hina eid(8874)e). Purpose
clause with hina and the second perfect active subjunctive of
oida, to know with settled intuitive knowledge. He wishes them
to have eternal life in Christ ( Joh 20:31 ) and to know that
they have it, but not with flippant superficiality ( 2:3ff. ).
{Unto you that believe on} (	ois pisteuousin eis). Dative of
the articular present active participle of pisteu(935c) and eis as
in verse  10 . For this use of onoma (name) with pisteu(935c) see
 3:23  Joh 2:23 .