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I think it is not absolute. What if the wallet in which you are storing your Bitcoins does not support the SegWit2x?

Keep private keys and you will be fine

Ok, so is the first Segwit fork that just happened (what was it... a month back?) going to remain it's own chain, seperate from Segwit 2X?

So we'll have, in total (not including earlier forks like litecoin): legacy bitcoin, bitcoin cash, bitcoin gold, Segwit and Segwit 2X. Is that correct?