If life consists of relationships, then truly Jesus gives us eternal life.
Jesus establishes our relationship with God -- our eternal relationship with the One who loves us fully. With that eternal relationship, we have eternal life.
"I came that they may have life, and have it abundantly." -John 10:10 (NAS)
As a corollary, consider what death is. You have probably heard that death is separation. With this thought, I can more clearly see that that is true. Death is the loss of relationship -- hence, separation. And eternal death would thus be the eternal loss of relationship. Perhaps a clearer picture of hell than most conceptions. [An idea found in C.S. Lewis' "The Great Divorce", by the way.]