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

king of the pile? wrote:

3/10

original post 1/10, but somehow 5-10 idiots posted on here

including me

shit

I think you mean 2.999... /10

Free Advice wrote:

When recording your time, as long as the first number you write down is a 3, then I think you're good.

Great news for me!

3/3 and .99999 might not be equal.

Just as 1/3 and .33333 and 2/3 and .66666 might not be equal to each other.

the 3:90 miler wrote:

Free Advice wrote:

When recording your time, as long as the first number you write down is a 3, then I think you're good.

Great news for me!

HAHAHAHAH!

a number wrote:

so wrote:

so if .8888888888... = .899999999999... = .9

doesn't .88888888... = .9?

.8888888888.. doesnt equal .8999999999.. it is smaller.

So if I run 3:59.888888... does that mean I've run a sub 4:00 mile, or is it smaller than sub 4:00?

Bowlician wrote:

3/3 and .99999 might not be equal.

Just as 1/3 and .33333 and 2/3 and .66666 might not be equal to each other.

Carried out to infinite, they are equal.

Guppy wrote:

This thread is great.

I agree. And we haven't even started talking about Zeno's paradox, which suggests that you can never actually get to the finish line of a one-mile race.

I seem to remember a thread like this a while back, but instead it involved Teg getting infinitely close to a 10K.

you wouldn't know if this happened. you would be given a time of 4:00.00. i think you would need to run 3:59.990 to be given a time lower than 4 mins. you have to be at least a hundreth of a second below it.

It all depends on your frame of reference. If you're talking in a track and field sense then no, you haven't.

3.59.99999 would be rounded up then you would not have broken 4. In the same way, consider the athlete who runs half his mile race in lane 2 and runs 4.00.00. Whilst he might have covered a mile exactly in under 4, within the rules of track and field he hasn't.

However, if you're speaking literally, then yes of course 3.59.9999 (mathematical arguements aside) means you've broken 4 minutes. The problem, as highlighted by my above example, is that no-one takes into account 'actual' times rather people refer to times as defined by the rules in the sport.

Assuming, as you do, that they are equal, then their equality is not part of the question, and we simply speak of two different representations of the same number. So your question essentially becomes, "does 4:00 break 4:00"? Hardly a question worth asking.Practically speaking, we do not have stopwatches with infinite resolution of time, and if we did, we can not ignore real world complications like Relativity (just who is doing the timing -- the runner or an outsider? Imagine breaking 4:00 and not breaking 4:00, with the same run!) and the Heisenberg Uncertainty Principle (can we really be certain of the speed and the position of the runner, at any instant?)

AC XC wrote:

since .9999999... repeating is obviously equal to 1, it follows that 3:59.9999... repeating is obviously equal to 4:00. I am sure this will have a great effect on the all-time sub 4 list, what you're opinions?

Funny, but you used two different numbers (count the nines), which are most certainly not equal.

Dave Wottle wrote:

.99999999999999999999999999999999999......is not equal to 1 however, it is equal to .9999999999999999999999999999

Some of you must have never taken a calculus class to know about limits. 3:59.999999 carried out with an infinite number of 9s is not 4:00. You can round up to it if you want, but that doesn't change the fact that it never truly equals or touches 4:00.

leaping lanny wrote:

Some of you must have never taken a calculus class to know about limits. 3:59.999999 carried out with an infinite number of 9s is not 4:00. You can round up to it if you want, but that doesn't change the fact that it never truly equals or touches 4:00.

Uh no, evidently you don't understand limits.

1/2+1/4+1/8+...=infinite, right? Wrong. It equals 1. Same thing here.

Ticktock wrote:

Uh no, evidently you don't understand limits.

1/2+1/4+1/8+...=infinite, right? Wrong. It equals 1. Same thing here.

The limit as it approaches infinity is 1, but it never actually equals 1.

try again, genius wrote:

AC XC wrote:

since .9999999... repeating is obviously equal to 1

Um no, it is obviously equal to .9999999 repeating. Not 1

See how that works?

LLLLLeeeeerooooooooooooooy mmmmmJeennnnnkkkinnns!

Did you pass calculus?

One only need to learn algebra to prove the equality.

From my notes, the sum of a geometric infinite series

∑ k=1,infinity (a*r^k)

can be easily rewritten: a*r/(1-r)

When a=9 and r=0.1, (i.e. 0.999...) we get:

9*0.1/(1-0.1)

= 0.9/0.9

= 1

You might want follow these links to learn something:

"http://en.wikipedia.org/wiki/Geometric_progression"

"http://en.wikipedia.org/wiki/Infinite_series"

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

You can cling to the inequality for all the fallacies stated in the links, but it's not supported by modern mathematics.

uh the limit of the infinite series is one but that doesn't necessarily mean the series will equal one. Walk halfway towards a door, then walk half of the remaining distance. Continue on, you will never reach the door. The limit of the steps you take is the door but you wont reach it.

0.9999 repeating does indeed equal 1. A simple proof is that no real number exists between 0.9999 repeating and 1. One of the properties of real numbers is that it is possible to find a real number in between any two different real numbers. Since no real number exists between 0.9999 repeating and 1, they must not be different.