[1 paradox] Why 0.999... is not equal to 1?
The equality 0.999... = 1 has long been accepted by mathematicians and is part of general mathematical education.
but 1 is a number in the finite world.
Quotebut 1 is a number in the finite world.1 is also a number in the infinite world.Mathematicians say finite world == N and the infinite == R N is a subset of R so all finite numbers are infinite too.
"From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2." --Volume I, 1st edition, page 379 (page 362 in 2nd edition; page 360 in abridged version). (The proof is actually completed in Volume II, 1st edition, page 86, accompanied by the comment, "The above proposition is occasionally useful.")