Even the hyperreal numbers *R, which include infinitesimals, define 1 == .999...
this post was submitted on 27 Jun 2024
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I can honestly say I learned something from the comment section. I was always taught the .9 repeating was not equal to 1 but separated by imaginary i ... Or infinitely close to 1 without becoming 1.
The way I see it is the difference between equal numbers is zero.
The difference between 0.999… and 1 is 0.000…, and since the nines don't end, the zeros don't end, so the difference is just zero.
Meaning 0.999… = 1