There is a substantial difference between infinity minus 1 and one less than infinity. Infinity is not a number therefore it cannot be subtracted. You are right that one less than infinity is still infinity however it is a different infinite set and cannot be compared with the old infinite set.Spencer Petersen said:
Poll: Does 0.999.. equal 1 ?
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I never claimed my calculator said 0.3 recurring. The fact that it did not was what made me learn that 1/3 = 0.333... because as I devided one by three, I tried to return to one by multiplying it with three again and ended up with a bunch of nines on the screen. I asked my parents about it and got the answer that it was because the calculator could not handle an infite amount of numbers and therefore made a small error.matt87_50 said:
Implying that the set of decimals will end 1 digit before the other set is also implying that either one will end at some point. Because they are infinite they will never end.Winthrop said:
I agree the proofs which work with statements like 1/3=0.(3) do not actually give new insights, but only show that the statement 1/3=0.(3) is equivalent to 0.(9)=1. However, I'd like to know what proof(s) you (or the mathematicians (what are their credentials by the way?) you know) can give that "1/3 is not .(3)".Winthrop said:
The function was never stated to us, so I was ASSUMING that it was discontinuous. If the function's really nothing more than f(x) = x , well, that changes things. I didn't read this thread all the way through because I found that doing so on the Escapist is a good way to get ulcers, but if he mentioned that the function is f(x) = x, then I retract my original statement.Zukhramm said:
IF the function is discontinuous, however, then there is potentially a very, very important distinction between x being less than 1 and x being 1, which anyone who went through a Calculus class on limits can understand.
Your proof is much better than most of the other proofs. However when working with an infinite set one more 9 will always be appended to the end of the equation. So the number between it and 1 would continually be itself. If that doesn't make sense I am sorry I am less confident in this then the counterexamples of the other proof. I agree that proofs can not exist for both sides, however I have found flaws in the proofs saying they are the same and have yet to find them in those supporting it. I merely supplied those because you implied I had no proofs to back my claims. My statement that by definition they are not equal is actually what is up for debate here so I apologize for using that as defense.Darth Crater said:
My brother is a math PHD and his friends have degrees in math(not sure what level sorry). They are the ones I was referring to. I do not have access to any of them atm so I can not provide you with there proofs however some of them are similar to the ones on this page http://en.wikipedia.org/wiki/User:ConMan/Proof_that_0.999..._does_not_equal_1#Proving_that_1_does_not_equal_.9.._using_the_definition_of_number_sets:karplas said:
Yes, it does, and there are a variety of ways to prove it (though I wont list them, the community here already has you covered from that aspect).
Only if you round. Even though the gap between 0.99 repeating and 1 is so incredibly small that is usually matters very, very little, it's still not 1.
Sorry to end this discussion so abruptly, but 0.9 recurring equals 1. It's got many mathematical proofs.
If you're theoretical and abstractly talking... then of course not, why have different definitions of the same thing. 0.999 is not 1, just as 0.999999 is not 0.999998.
Also equals can be reversed, does 1 equal 0,999?
But if it's something domestic, like measuring your wang, then why not?
In simple math, anything over 0,50 is 1, and under 0,49 is 0.
Also equals can be reversed, does 1 equal 0,999?
But if it's something domestic, like measuring your wang, then why not?
In simple math, anything over 0,50 is 1, and under 0,49 is 0.