<p>I would really like a MIT student to post there what they think, as they will actually know what they are talking about. </p>
<p>I say it doesn't, by the way</p>
<p>No..............</p>
<p>Durran, will you post in the other thread too please?</p>
<p>My opinion: no. As posted on other thread.</p>
<p>It does. I think.</p>
<p>HAHAHA LOL .... This is a huge debate for some people...especially at my HS.
My opinion...No</p>
<p>I remember a 30 page topic on this at gamedev, and eventually, somebody got a link to a proof.</p>
<p>On another note, I don't rememeber whether the final answer was yes or no.</p>
<p>My opinon is yes though.</p>
<p>Here is my proof:</p>
<p>.9999999... = .9 + .09 + .009 + .0009 ...</p>
<p>so we can have a series:</p>
<p>(9/10) * sum( from n = 0 to infinity, .1^n)</p>
<p>This is that special series(can't believe I forgot the name, swear it's geometric or something) where you can compute the sum using the formula with:</p>
<p>a/(1 - r)</p>
<p>where a = 9/10
and r = .1</p>
<p>so we have</p>
<p>(.9)/(.9) = 1</p>
<p>i think that
.9999... will never be equal to 1 without intervention</p>
<p>what is infinity? that's what ppl made up to use limits and eventually differencials and integrals.</p>
<p>but, really, when does infinity become an infinity? im pretty sure that there is a number before. if so, we could add as many numbers as we want to that, first, number and still get a finite result</p>
<p>im not sure what i meant there^ lol, but my point is that one can always make an infinity finite he-he</p>
<p>so, .9999999.....would be always a finite number (sounds weird) and thus, would never be equal to 1</p>
<p>i do gree though, that the LIMIT of .99999....would be equal (i'd rather say APPROACH) to 1
but the number .99999..... -- no way:)</p>
<p>btw, how do you quote somebody? :)</p>
<p>I will explain, give me 10 minutes.</p>
<p>PS: The answer is YES. Almost unambiguously.</p>
<p>Actually, it will be easiest if you just read this thread:</p>
<p>The answer is YES, assuming we use the standard metric on real numbers.</p>
<p>Sagar Indurkhaya is correct.
It is out of the question.-as logic serves</p>
<p>You might think about it as the hotel with infinite number of rooms(those who are interested in math will know about this analogy).--look at "Fermat's last theorem;by Simon Singh --</p>
<p>There was a semi correct solution shown to me in 4th grade-i think-</p>
<p>6/9= .666666666...
5/9=.55555555555...
8/9=.8888888888...
9/9=.999999999999...=1</p>
<p>i am applying to MIT stanford...-total 5 schools-
2240+800+800+780(math 2,chemistry,mol bio)</p>
<p>wish me luck</p>
<p>take care all.</p>
<p>Read through the thread I linked. It will address any disbelief you have. The result 0.999... = 1, is true and undebatable. Unless you redefining the number 0.999..., or the metric, which of course proves nothing.</p>
<p>.999... is equal to one. Take a piece of chocolate, cut it into 3 pieces, and you have 3 peices of .3333....</p>
<p>If you put them all back together, you get .999..... which should be 1 since you have the same amount of chcolate</p>
<p>ok...i've looked through that thread...
to tell you the truth, i didnt get a lot from there....he-he...i'm stupid lol</p>
<p>for me (and as Icarus said) infinity is just a CONCEPT...there is no such thing as infinity...(in real world)</p>
<p>so they say that .9999999....is not a real number b/c it goes to infinity, and they also say that REAL numbers can't go to infinity...
ok..i got that point</p>
<p>what's 1 then? can we represent 1 as 1.00000.... i think yes. so now this number also becomes NOT real and we can compare 1.000....with .9999....
in 1.0000... zeros would go and go forever (i dont mean that forever=infinity)
in 0.9999... nines would go and go forever</p>
<p>so there would be always some interval between them (even if this interval IS unreal)</p>
<p>.999... IS a real number, because it is equal to 1, which is a real number. They are both representations of the same real number. There is no interval between them because there is no real number between .999... and 1, therefore they are the same number.</p>
<p>Yep, .999... definitely equals 1. say .999... = x, then 9.999... = 10x. if we take the difference, we get 9x = 9, which means x =1. therefore, .999...= 1.</p>