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We have in PIE:

e̯eitr way, pedestrian road

e̯imos road

e̯iera̯ year

e̯eiti goes

e̯iteros other, another, next

I wonder whether the word for "one"

e̯oinos alone, separated

connected to the above?

Note that the PIE word e̯oinos had clear meaning of "one alone", "one separated" contrasted with another word for "one", som which meant "united", "one together".

There was also word for "thus", "ergo", "it follows that" which confusingly Mallory gives as e̯ita̯ while Beekes gives as e̯ei and analyses as locative case of pronoun e̯e "that".

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No, as far as we know to this moment it is not.

The word "один" is related to this PIE root (*h₁ey), and the word "идти" - to this one, which also is transliterated like (*h₁ey), but this is a coincidence. Personally I never've heard such assumption.

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