This text, Jn. 17:9, is used as an argument for strict limited atonement. There are no scriptural texts that teach that Christ died ~only~ for the elect. Strict Limited Atonement (SLA) advocates use Jn. 10:11 in an attempt to show this, but it does not say that He ~only~ gave His life for the sheep. To argue otherwise is a negative inference fallacy.
The SLA advocate uses Jn. 17:9 to argue, "if Christ died for the world, then surely He would pray for the world. He specifically does not pray for them, so He didn't die for them."
But He did pray for the world in Jn. 17:20-23.He prayed things appropriate for them - that the world would believe.
"I do not pray for these alone, but also... that the world may believe that You sent Me... and that the world may know that You have sent Me, and have loved them as You have loved Me."
Verse 9 is addressing His immediate followers, who were with Him (v. 12). Verse 20 confirms this when He prays for those who in turn believe His follower's words.
He prays for specific things that are appropriate for each group.
For His followers He prays for God to keep them, that they be one as They are, that they may have Christ's joy, that they be kept from the evil one; and that they be sanctified.
For those who believe through their word He prays that they be one.
For the world He prays that the world would believe that He was sent by God.
So, it just is not true that He does not pray for the world at all. He prays for each group. This argument for strict limited atonement, based on Jn. 17:9, is not a valid one.