Poll: 0.999... = 1
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You misunderstand how variables work. The variable has only one value at a time, but can have an infinite amount of values. So in this case, the solutions for x[sup]2[/sup] = x are, indeed, x = 0, 1.emeraldrafael said:
0[sup]2[/sup] = 0
1[sup]2[/sup] = 1
QED.
Would you kindly provide this 'very very slight' difference between 1 and 0.(9)? I'm very very much interested in seeing it.SomethingAmazing said:
I won't be surprised at all if said difference is 0.
No matter how many threes you have, it still won't quite be a third. Sorry.BlacklightVirus said:
Ok for simplicities sake and to end this arguement
x=.99999 (the amount of nines doesn't matter it is true for any number of nines, I'm just truncating at a smaller amount of nines.)
10x=9.9999 (this is the step that everyone gets wrong as multipling (.9*.1^n)! by 10 gets (9*.1^n)!, not (9*.1^(n+1))!. (9*.1^(n+1))! is 9.99999 when n+5)
thus 9.9999-.99999=8.99991=9x
8.99991/9=9x/9,8.99991/9=.99999
QED x=.99999.
Try this with a calculator for any amount of nines and you'll see that my math is right.
x=.99999 (the amount of nines doesn't matter it is true for any number of nines, I'm just truncating at a smaller amount of nines.)
10x=9.9999 (this is the step that everyone gets wrong as multipling (.9*.1^n)! by 10 gets (9*.1^n)!, not (9*.1^(n+1))!. (9*.1^(n+1))! is 9.99999 when n+5)
thus 9.9999-.99999=8.99991=9x
8.99991/9=9x/9,8.99991/9=.99999
QED x=.99999.
Try this with a calculator for any amount of nines and you'll see that my math is right.
Ok i completely agree with this point that 0.999... = 1 and i have had it proven to me by one of my maths professors in a way that has been said earlier in the thread, the one that states that if 1 =/= 0.999..., what is the number in between?, but my point here is, i don't see a poll in this thread.
A tempting fairytale, but nonsense. If x is in S, then x = y implies y is also in S. 0.33(3) is also a rational number, because it's the exact same thing as 1/3. By the same reasoning, 1/3 is also a real number. Of course, all rational numbers are also real numbers, so that was obvious anyway.IMakeIce said:
Your general point is okay though: these numbers are entities that operate under strict predefined rules. If you don't follow the rules when manipulating them, you're going to end up with nonsense.
I bolded the problem for you. You can't do any of this with a calculator, because a calculator can only deal with finite numbers of decimals. We're talking about the nines going on for infinity, in which case there is no infinity - 1, because that is still infinity, which can't be represented with a calculator.Sprntr_Zomby said:
I think you're trolling. 1/3 will always be less than 1.(3). That's a mathematical fact.PoisonUnagi said:
I think he meant to say 0.33..., not 1.33...BlacklightVirus said:
I don't think anyone would argue that 1/3 > 1.333..., but arguing that adding threes to the end of 0.33 will always be less than 1/3 makes more sense.
I still want an answer to my previous question.
Any repeating decimal is a rational number and can be expressed as a fraction, by definition.
What fraction equals .99...?
Any repeating decimal is a rational number and can be expressed as a fraction, by definition.
What fraction equals .99...?
You know, come to think of it, I'm surprised that web forums don't have some kind of automatic function to destroy threads like this at inception.
Blizzard literally had to start banning people to stop this conversation clogging the battle.net forums when they posted the proof as an april fools joke years and years ago. I don't know if the april fools joke was that the proof was real...or that they knew people would go ape!@#! over it...
Blizzard literally had to start banning people to stop this conversation clogging the battle.net forums when they posted the proof as an april fools joke years and years ago. I don't know if the april fools joke was that the proof was real...or that they knew people would go ape!@#! over it...
no, the problem is that you said 1/3 > 1.333...PoisonUnagi said:
1/3 = .333...
and
.333... < 1.333...
so you're typo made you look like an idiot
YOU FOOL! we're humans logic does not apply to us!Rabid Toilet said:
actually since .999... is the series (.9*.1^n) you can choose any value and cut it off with slightly more error room. In my discrete math class last semester my class of 20 student spent about 10 hour each proving out from 0 to several thousand that this series work and does converge to .999... not to 1. As you head out to infinity x heads to .999... it never reaches one.