Does 0.999... = 1?

<p>faBELLA_regina: I didn't say anything even remotely resembling that.... :?</p>

<p>yeah, because like every mathematician must be wrong on something this trivial.</p>

<p>oops im so sorry, ok i see..you didnt use quote's, it looked like part of your post ;P my bad</p>

<p>it was plagmayer that said it</p>

<p>Wow you guys are nerds. :)</p>

<p>But then again if this was a post concerning something to do with History, I'd be just as much of a nerd.</p>

<p>Some people here have a hard time dealing with infinite. Does that mean that you do not understand Zeno's Paradox either?</p>

<p>^^People fail to grasp the idea of infinite. Like 0.9999...=1 can be proven true with an infinite geometric series, Zeno's Paradox can be explained.</p>

<p>My statement: .999...=1.</p>

<p>My proof: I got into MIT.</p>

<p>I win =)</p>

<p>Eighteenforluck: That doesn't make you win :)</p>

<p>I love Zeno's Paradox... my friends and I had quite the argument over it one night after the movies in the theater parking lot. It was hard for people to grasp but once they got the concept, it made sense in a... paradoxical manner (but the slow guy can't win!! The fast guy is faster!).</p>

<p>The idea behind the paradox: Let's say you have a given distance. There's a turtle and hare having a race. The turtle says, "I can totally own your face if you give me a head start". The hare's like "kthx go for it n00b". So the turtle gets a bit of a head start and the hare goes shortly thereafter. </p>

<p>Can it be proven that the turtle indeed wins?? Let's say the turtle gets a 5m head start. By the time the hare travels 5m, the turtle has already traveled more than 5m and is thus adding more distance for the hare to travel. In a sense then, the hare is always "catching up" and the turtle is always ahead. Thus the turtle must win.</p>

<p>But how can that be so? We know empirically that the hare should win! He's faster.</p>

<p>The primary misconception that makes this paradox able to confuse so many people is derived from a faulty understanding of infinity. Not all infinite sums are the same and this is what throws people off.</p>