On the nature of Omniscience
This is a discussion that takes place between King Pasenadi of Kosala and the Buddha. Here the King asks:
"I have heard it said that: 'The recluse Gotama speaks thus: "There is neither a recluse nor a brahman who, all-knowing, all-seeing, can claim all-embracing knowledge-and-vision - this situation does not exist'"
'The recluse Gotama says: "There is no recluse or brahmin who is omniscient and all-seeing, who can claim to have complete knowledge and vision; that is not possible."'
Bhikkhu Thanissaro has:
"Lord, I have heard that 'Gotama the contemplative says this: It is not possible that a priest or contemplative would claim a knowledge and vision that is all-knowing and all-seeing without exception.'"
The expression in Pali:
Na'tthi so sama.no vaa braahma.no vaa yo sabba~n~nuu sabbadassaavii aparisesa.m ~naa.nadassana.m pa.tijaanissati...
All-omnicient, all-seeing, (apara > after > April > afar) continuous/sequential one after the other knowledge and vision
The Buddha states that he did not say this this way, and the King asks him in what way this might have been said and misunderstood. The Buddha explains:
"I, sire, claim to have spoken the words thus: 'There is neither a recluse nor a brahman who at one and the same time can know all can see all - this situation does not exist."
"I recall having actually made the utterance in this way, great king: 'There is no recluse or brahman who knows all, who sees all, simultaneously; that is not possible."
They site: MA:
There is no one who can know and see all - past, present, and future - with one act of mental adverting, with one act of consciousness; thus this problem is discussed in terms of a single act of consciousness (ekacitta). On the question of the kind of omniscience the Theravada tradition attributes to the Buddha, see n. 714 (which follows in reference to a similar question asked by Vacchagotta: "... The part of the statement that is valid is the assertion that the Buddha is omniscient and all-seeing; the part that is excessive is the assertion that knowledge and vision are continuously present to him. According to the Theravada tradition the Buddha is omniscient in the sense that all knowable things are potentially accessible to him. He cannot, however, know everything simultaneously and must advert to whatever he wishes to know. At MN 90.8 the Buddha says that it is possible to know and see all, though not simultaneously, and at AN #24/ii24 he claims to know all that can be seen, heard, sensed, and cognized, which is understood by the Theravada tradition as an assertion of omniscience in the qualified sense."
"Great king, I recall having said, 'It is not possible that a priest or contemplative could know everything and see everything all at once.'"
In Pali the Buddha constructs it this way:
Na'tthi so sama.no vaa braahma.no vaa yo sakideva sabba~n~nassati sabba.m dakkhiiti, n'eta.m .thaana.m vijjatiiti.
Sakid'eva: at once
 The story of the evolution of King Pasenadi from scoffer to devout follower is another of the fascinating stories that one sees developing over the course of reading the suttas.
 maharaja: great king
 The Nanamoli/Bodhi version of the Tevijjaman idea:
From: Majjhima Nikaya I, #71: Tevijja-Vacchagottasutta;
PTS, Horner, trans, To Vacchagotta on the Threefold Knowledge, pp160;
WP, Nanamoli/Bodhi, trans, To Vacchagotta on the Threefold True Knowledge, pp 588
When Vacchagotta asks The Buddha how it would be proper to describe what Gotama would claim to know:
N/B: "Vaccha, if you answer thus: 'The recluse Gotama has the threefold true knowledge,' you will be saying what has been said by me and will not misrepresent me with what is contrary to fact. You will explain in accordance with the Dhamma in such a way that nothing which provides a ground for censure can be legitimately deduced from your assertion.
"For in so far as I wish, I recollect my manifold past lives, that is, one birth, two births . . .(as Sutta 51, Ii24) . . . Thus with their aspects and particulars I recollect my manifold past lives.
"And in so far as I wish, with the divine eye, which is purified and surpasses the human, I see beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate, and I understand how beings pass on according to their actions . . .(as Sutta 51, Ii25) . . .
"And by realising for myself with direct knowledge, I here and now enter upon and abide in the deliverance of mind and deliverance by wisdom that are taintless with the destruction of the taints."