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I understand that cosmic microwave background radiation is remnant of the universe after 380,000y of the origin.

To me, this radiation is still a wave which has a microwave frequency and I also understand that if we look at the frequency of wave, each sec, frequency gets decreased - this is due to redshift. I also get that it's coming from every direction which is one of the biggest reason we can say it is what it is we call it.

Now, how do we know with this wave, that it's the wave coming from after 380,000y of the universe ? why can't it be from after 900,000y.

I read some stuff, but all they mention is, we did some calculations and observations with COBE, but still, I don't get it how we arrived to the conclusion that it's coming from that time of 380,000y.

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