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I am X. I was roaming around some place and found another X. We got attracted. Got into some operation and generate Y.

At first Y is 0

Me and my X got together now and went to roam the places.

We are now 2X

We found the group of X with the same number of members as ours and also got into some private operation and got another Y.

We have Y+1

Now, we all X's got together and the same process happened, got Y and again went around with all the X's.

Now tell me What am I?

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  • $\begingroup$ Rot13$[$Sbe gur svefg cneg, gur bcrengvba pbhyq or "fhogenpgvba" fvapr K-K=0 juvpu jbhyq rdhny L va gung pnfr.$]$ $\endgroup$ – Mr Pie Jul 10 '18 at 11:57
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    $\begingroup$ Time for a hint, please. $\endgroup$ – MichaelMaggs May 2 at 13:15
  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it. If not, a response to the answerer to help steer them in the right direction would be helpful. $\endgroup$ – Rubio♦ May 7 at 4:55
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You are

a vector, roaming somewhere such as the plane.

At first Y is 0

You are aligned with and opposite to the other X

We are now 2X

You are aligned with and in the same direction as the other X

We found the group of X with the same number of members as ours and also got into some private operation and got another Y.

You’ve engaged in matrix operations, maybe multiple times.

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