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I have been since nearly the beginning.
I endure nearly to the end of all time.

At first, I was the one that came after.
Now, I am the one that comes before.

I am $-1$.
I am $3$ of $7$.
I am sometimes confused for $5$ or $22$.
If $n$ is an integer, I am $2n -1$.

I might be cut off the middle.
I might be part of an event, or merely part of the countdown.
I might be found in a lost flight of birds.
I might be the first and last thing you ever achieve.

What am I?

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18
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You are

EVE


Clues:

I have been since nearly the beginning.

Refers to the biblical Eve

I endure nearly to the end of all time.

EVE(-r)

At first, I was the one that came after.

Again, the biblical Eve, who came after Adam

Now, I am the one that comes before.

Eve as in the day before, like today (X-mas eve, which also explains the title)

I am −1.

If today is $0$, then eve is $-1$ (alternatively, the date of the eve is one less than the date of the actual day)

I am 3 of 7.

Three letters of sEVEn

I am sometimes confused for 5 or 22.

EVE can be anagrammed to VEE (V, five in Roman numerals, or the 22nd letter)

If n is an integer, I am 2n−1.

$2n$ is even, so $2n-1$ is EVE(-n)

I might be cut off the middle.

sEVEr (thanks @Ankoganit)

I might be part of an event, or merely part of the countdown.

EVEnt, or part of the countdown to the following day (thanks @Rubio)

I might be found in a lost flight of birds.

A flight of birds forms a VEE-shape, which anagrams (lost, in the confused sense) to EVE (thanks @Ankoganit)

I might be the first and last thing you ever achieve.

EVEr achiEVE

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  • $\begingroup$ "Cut off the middle" may be sEVEr, "lost flight..." may be referring to the 'vee'-shape of flight of birds. $\endgroup$ – Ankoganit Dec 24 '17 at 9:14
  • $\begingroup$ @Ankoganit ah, sEVEr fits better. Not sure about "lost flight..." but your suggestion sounds plausible. Thanks! $\endgroup$ – Volatility Dec 24 '17 at 9:55
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    $\begingroup$ If 2n is even, 2n-1 will be odd. $\endgroup$ – prog_SAHIL Dec 24 '17 at 10:26
  • $\begingroup$ @prog_SAHIL this is tagged wordplay though, not mathematics $\endgroup$ – Volatility Dec 24 '17 at 10:30
  • $\begingroup$ @Volatility I know that. Thats why I gave this an upvote. Seems very logical and appealing to me. :) $\endgroup$ – prog_SAHIL Dec 24 '17 at 10:47

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