The use of the word in a few places of Scripture
The Greek language employs at times a double negative, greatly intensifying the force of the expression used; and when the matter asserted involves a question of duration, the addition of a phrase significant of eternity takes away from such duration all limit whatever.
There are some six places in the New Testament where we get the negative with a term of eternity attached, in five of which the negative is doubled. The places are Mark 3:29; John 4:14; 8:51; 10:28; 11:26; 13:8. Passing by the last of these, we may look at the other five; and we shall, I believe, be led thereby to adore afresh the gracious Spirit who wrote these things for our learning, that we, through patience and comfort of the Scriptures, might have hope.
says, "Whoever drinks of the water that I shall give him will never (οὐ μὴ) thirst.” One might perhaps show the exact force of the expression used thus - "shall not, no, he shall not thirst for ever." The drinking and the fresh, full satisfaction from the ceaseless, boundless supply continue for ever and ever.
has it, "If a man keep My word, he shall never (οὐ μὴ) see death" - "he shall not, no, he shall not see death for ever." Such is the power of the word of Christ received, retained, and observed; it conveys to the receiver, and effects in him its own object, with vigour which even eternity does not diminish. "The words which I speak unto you," says the Lord, "they are spirit and they are life." Whosoever has been laid hold of by them must, through their operation within him, have life co-existent with the words by which he has been laid hold. They impart to him their own character.
In we have, "And I give them eternal life, and they shall never (οὐ μὴ) perish", thus "they shall not, they shall not, perish for ever." The acquisition of eternal life, as given by the Second Man, the quickening Spirit, is accompanied with the complete impossibility of perishing. This is a life which never wanes, never decays. He who imparts it is Himself its source and supply. That which He gives must, alike with that which He speaks, be in correspondence with Himself. He is the Way, the Truth, and the Life.
So once more in John 11:26, "Everyone who lives and believes in Me shall never (οὐ μὴ) die" - "never, never die."
Thus are these words of the Lord Jesus Christ presented to us like His "most assuredly” (verily, verily in the KJV - ἀμὴν ἀμὴν e.g. John 5:24) a duplicated witness, a confirmation with an oath of the acceptance and security of all to whom they refer. "Thanks be to God for His unspeakable gift."
Of course one does not need “no not” for the Holy Spirit to stay “never” – there are other forms of the Greek.
In we read, “but he who blasphemes against the Holy Spirit never (οὐκ ἔχει - will not) has forgiveness, but is subject to eternal condemnation". Here we do not have a double negative but rather “not” that denies absolutely and categorically. The attribution to Satan of the works of Christ involved those who made it in eternal sin - sin from the judgment of which there was no escape.
Modified from The Christian's Friend (1898): "Never" ANON
 οὐ (ou – this is the basic Greek particle that represents some form of “no” or “not” in our English translations, as well as a multiple form of combinations that reflect the negative in some form or other.
μη (me) – this is the other Greek particle that represents “no” or “not,” and it too has a variety of forms that it occurs in reflecting the negative. However, there is a difference in the application of ο? (ou) and µ? (me).
Thayer notes: that οὐ denies the thing itself (or to speak technically, denies simply, absolutely, categorically, directly, objectively), but μη denies the thought of the thing.
http://blogs.blueletterbible.org/blb/2012/05/23/emphatic-negations-in-biblical-greek/ (accessed July 2018).
 William Mounce explains that οὐ μὴ (ou me) does not mean ‘never’ in and of itself. However, when you have οὐ μὴ in combination with the aorist subjunctive, it is implied that something cannot ever happen. https://www.billmounce.com/monday-with-mounce/translating-all-the-words-scripture-matt-24-34 (accessed July 2018)
The double negative appears in 80 verses in the New Testament. One which all Christians hold to is: Hebrews 10:17 - "their sins and their lawless deeds I will remember no more" being the essence of the gospel.
 In the original article the author implies a οὐ μὴ in Mark 3 when it is not so – however οὐκ can be rendered "no, not". The Greek reads: , οὐκ ἔχει ἄφεσιν εἰς τὸν αἰῶνα (transliterated: never has forgiveness to the eternity [or all time])