Quote:
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Originally Posted by Grommit
Mathematicians would agree that .999... and 1 represent the same real number. In fact, from my real analysis book, "Elementary Analysis" by Kenneth Ross, it says:
[short proof, similar to above]
"Thus 0.9999... and 1.0000... are different decimal expansions that represent the same real number!"
Later on the book proves that the only case where this can occur is when the two expansions for the same real number end in an infinite series of nines and infinite series of zeros.
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Real number...yes.
That's because you can't have decimals and fractions in a real number...so I guess you could say yes, .999~ and 1 are the same real number.
[Edit: Wait...just kidding. Im dumb.]