Is running 3:59.99999... in the mile actually breaking 4:00

great because i ran 3:87 last week!

simple wrote:

It's pretty simple logic....is 3:59.99(repeating) faster than 4:00.00? No matter how insignificant the difference it IS faster, thus it IS breaking four.

Faster, huh? By how much?

Exactly.

story prob bob wrote:

I have no math background so the all mighty ones who do please have mercy. I liked the comment about those ignorant fools probably thinking the earth was round.

Anyhow my simple/dumb observation is this: .9 is not 1. .99 is not 1. .999 is not 1. Why would .9 repeating be any more "1" than those figures? It won't hit a magical digit and suddenly be one. If it's because the adding can be infinite, why can't something else in math be infinitely close to something without being it?

There is that kind of thing that is infinitely close called infinitesimals but they are not real numbers. .999.. is a real number the same one as 1. .999.. repeating is not the same one as .99..9 stopping so there is no obvious reason why it couldnt be 1. Why it actually is the same as 1 is because that is how the real numbers are defined they are defined so that the infinitely close things are equivalent.

Troll

This is the easiest way of understanding

x=0.99999.....

10x=9.999999......

9x=10x-x

9x=9.999999...... - 0.999999....

9x=9

x=1

Therefore 0.99999.....=1

decimals are APPROXIMATIONS.

.999 = 999/1000

&

1 = 1000/1000

...there's a difference.

3:59.9bar is a sub-four mile.

uggh wrote:

decimals are APPROXIMATIONS.

.999 = 999/1000

&

1 = 1000/1000

...there's a difference.

3:59.9bar is a sub-four mile.

NO THEY AREN'T. They are representations. What the hell is .999 APPROXIMATING?

For all the idiots like you who claim 9bar doesn't equal 1, why don't include your academic credentials? I did my undergrad and masters in mathematics btw, and as many people have pointed out 9bar = 1. If you can't wrap your mind around this basic concept after the explanations given here, I suggest you go back to reading poetry and flipping my burgers.

What is causing some confusion is that you guys are trying to treat time as discrete, which it is not. You don't count down from 3.99999999999 to 3.99999999998 to 3.99999999997, etc. A continuous concept such as time can only be fully represented using limits, that's why it is valid to take the limit of 3:59.99999... and consider it 4:00.

I know this may seem confusing to some of you, so I'll just ask you to trust me here.

Well in technical terms doesn't a stopwatch count .95 to .96 to .97 to .98 to .99 and so forth. Therefore couldn't the same be said for if a stop watch actually went out to the thousandth or does the counting of actually stop at a certain decimal place.

I am with the poster who said that anything to infinity can not be proven which in reality would make any math concept a theory. The concept of repeating decimals to infinity had to originated by a person what makes you guys to so gungho to believe that person.

What about .333.. repeating? That is 1/3. But if you take it to be .3 = 3/10 or .33 = 33/100 or .333 = 333/1000 or .. eventually you have to stop and you never get to 1/3. So is .333.. repeating really 1/3 ?

As previously stated, based on the precision of electronic timing and rounding rules, 3:59.990 and under would be sub-4. And while this mathematical discussion of infinitesimals is quite illuminating, you would run into a physical limitation well before that: Planck time, which is the smallest unit of temporal measurement in quantum mechanics (less than 10^-43 s). And from a practical standpoint, the smallest unit that has been measured to date is much larger, on the order of 10^-18 s. Man, this nerdery is killing me.

I have to admit, as another finance guy, I find the math really interesting on this thread, even though it's a little over my head haven only taken a couple terms a calculus, which I barely remember. So, mathematically, here is what made the most sense to me, someone asked what exactly you could add to 3.999bar to equal 4, well

3.9+.1=4

3.99+.01=4

3.999+,001=4

But, it's impossible to put a 1 at the end of infinity, because there is no end to infinity, so

3.999bar+0.000bar=4 or 3.999bar = 4

Anyway, none of these things matter, because the rules of track and field govern over the rules of math when deciding if you've broken 4, and they round round up, so even if you believe that 3.9999bar is less than 4, you didn't break it, because those are the rules of the sport.

This all may sound more profound right now than it is because I'm about finished with a 22 of stone ruination IPA, and the only equation that I know for sure is

Beer=delicious

to the guy who says no motion occurs in intervals shorter than the Planck time, that is a contentious point and we don't have any empirical evidence for it. quantum field theory has perfectly continuous symmetries under translation and boost, so what you're describing could only be some aspect of a quantum theory of gravity.

has anyone studied non-standard analysis? I haven't, but I wonder whether 3.99999... and 4 are different in the hyperreals.

I didn't imply "no motion occur[ing] in intervals shorter than the Planck time," I merely stated that it was the shortest distance that makes sense in quantum mechanics and current physical theory. As I said, practical measurement errors make it irrelevant for the purposes of the original question (or at least as irrelevant as the 9-bar topic). In fact, the experimental uncertainty for the constant G is the primary issue. It's about one part in 1E5, whereas h is known with much greater precision and c is exact in SI. And if you're taking offense to the lack of empirical evidence for Planck units, to be fair you should apply that skepticism to the rest of QM as well. Furthermore, you'd be best served by conducting that debate at an institution of higher academic repute than this freaking website.

Ah, this topic is hilarious. I keep reading about ten normal responses, then getting to one that suggests 3.9bar and 4.0bar are different numbers, at which point I howl in laughter.

http://en.wikipedia.org/wiki/0.999

...

Q: How many LetsRun mathematicians does it take to screw in a lightbulb?

A: 0.999999….

oooh man. pulling out some wikipedia.

sooo credible. i completely believe you now that a wiki article backs you up.

meichenl wrote:

to the guy who says no motion occurs in intervals shorter than the Planck time, that is a contentious point and we don\'t have any empirical evidence for it. quantum field theory has perfectly continuous symmetries under translation and boost, so what you\'re describing could only be some aspect of a quantum theory of gravity.

Oh I know, I was just trying to frustrate the math guys. They also forgot to consider relativity...was the OP asking about the time on his wristwatch or the official time?

the real question is was it a mile or 1600 meters ;)

meichenl wrote:

has anyone studied non-standard analysis? I haven't, but I wonder whether 3.99999... and 4 are different in the hyperreals.

I've had just one lecture on it, so I'll keep the nerdyness going...

If the number of 9s after the decimal is an infinite hyperinteger, then 3.999... is strictly less than 4, differing by an infinitesimal hyperreal.

People have been posting some mathematical "facts" on this thread, but in math any fact always needs a note of how the rules were set up. In real number rules 3.9bar = 4.

This thread is hilarious.

I can just imagine a bunch of stud Football, Baseball, B-Ball, Hockey...even Curling players...

Sitting around masturbating math on a chat board.

This is why behind the scenes the Athletics press and media refer to you all as "Track Weenies."

It is simple, if the meet officials notify my that I ran a time under 4 minutes... I mindless yell in celebration with my buddies. And then I go and have marathon sex with my girlfriends.

But I guess you fwits wouldn't know much about that.

Sincerely,

Championship Athlete. (Galen Rupp, Hussain Bolt)