Hell is separation from God for eternity .
Any disagreement on that ?
It's not eternal life as an eternal life with the Father, but that of an eternal torment in the sense of spending an eternal miserable existence being tormented day and night. Scripture never calls it an eternal life in the lake of fire, but that of damnation as the scenario would be that of the complete opposite of the eternal life with Christ. Existing is still life, whether it be a glorified life with Christ in the New Jerusalem or one of damnation and torment in the lake of fire as both are eternal.
One needs to define a word to understand what it means. Scripture never says what we will look like in the resurrection of life or damnation. Matthew 13:36-42 speaks about the tares being the children of the wicked one who would be Satan and says they will be cast into a furnace of fire where there will be weeping and gnashing of teeth from those who are cast into the lake of fire so that one verse alone shows me they will have some kind of existence, but no one knows what they will look like. The rest of these verses are pertinent to that of the resurrection of life both in the New Jerusalem and the lake of fire.
Exist: to have actual being or reality; to live
Existence: the fact or state of existing, living or occurring the manner of existing
Genesis 2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
Ecclesiastes 12:7 Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it.
Here dust + breath from God = a living soul. When the flesh dies physically it returns back to the dust of the ground and our spirit is preserved with God for final judgment.
John 5:28 Marvel not at this: for the hour is coming, in the which all that are in the graves shall hear his voice,
John 5:29 And shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation.
1Co 15:50 Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption.
1Co 15:51 Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed,
1Co 15:52 In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
Mat 13:40 As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world.
Mat 13:41 The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity;
Mat 13:42 And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth.
Act 24:15 And have hope toward God, which they themselves also allow, that there shall be a resurrection of the dead, both of the just and unjust.
Rev 20:12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
Rev 20:13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
Rev 20:14 And death and hell were cast into the lake of fire. This is the second death.
Rev 20:15 And whosoever was not found written in the book of life was cast into the lake of fire.
One can not compare eternal life with the Father with eternal damnation in the lake of fire except that the two are opposite from each other. Those who are resurrected to be with the Lord will have an eternal life (existence) basking in Gods glory. Those who are cast in the lake of fire will not literally be consumed by an eternal literal fire as fire here means torment, destruction or as being destroyed or broken down like someone saying that we are going to destroy you and drag your name through the mud. They are not literally destroyed, but brought down to a lower level. Those in the lake of fire will have an existence of weeping and gnashing of teeth for the destruction and torment they will face for eternity. Death means separation from God as their eternal destiny (life) is the lake of fire. If death here meant not to exist anymore than what would be the purpose of the the second death and being resurrected to stand in the great white throne judgement. Couldn't God just make them vanish as if they never existed in the first place!
You keep saying death is an existence and if one is existing then it has to be some form of life. Not like the life we have now as being alive here on earth, not like eternal life with the Father, but yet a form of a tormented eternal life of existence in the lake of fire for eternity. We know flesh and blood can not inherit the kingdom of God and many will be alive when Christ returns. Those who have physically died in Christ will be changed in a twinkling of an eye to meet Him in the air just as we who are physically alive will be gathered with them, but yet we do not know physically what we will look like for many will be only dust in the ground when they are resurrected to be with the Lord forever. Those who have physically died and have no part of the inheritance also will be only dust in the ground depending how long they have been asleep, but yet will be transformed and meet those who are alive to stand before God in His great white throne judgment and will be cast into the lake of fire. There existence will be an eternal life of torment being separated from God forever. Scripture also calls it outer darkness and in my own minds eye I see it as not only being separated from God for ever, but like looking through a window in all their torment seeing that God does exist and they will never be a part of His glory. Eternal death is separation from God, but yet as we see in scripture they do exist in a tormented state forever as one has to have some form of life to exist even though it is not like the physical life we have now as all will be changed in a twinkling of an eye, but yet no one knows what anyone in Christ or those separated from Christ will look like.
God gives us a description as in fire and brimstone which can be used literal as in Sodom and Gomorrah burned to ashes and as a metaphor for torment, suffering, punishment or as Matthew 8:12 describes it as outer darkness. The New Testament description is a bottomless pit (abyss) (Revelation 20:3), a lake (Revelation 20:14), darkness (Matthew 25:30), death (Revelation 2:11), destruction (2 Thessalonians 1:9), everlasting torment (Revelation 20:10), a place of wailing and gnashing of teeth (Matthew 25:30), and a place of gradated punishment (Matthew 11:20-24; Luke 12:47-48; Revelation 20:12-13), everlasting fire Matthew 25:41, everlasting punishment, Matthew 25:46, lake of fire burning with brimstone.
Ecc 9:5 for the living know that they shall die: but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten.
Psa 104:29 Thou hidest thy face, they are troubled: thou takest away their breath, they die, and return to their dust.
Dan 12:2 and many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt.
James 2:26 for as the body without the spirit is dead, so faith without works is dead also.