???? 3.59.9999999 is NOT equal to 4.00.
4.00 is equal to 4.00 - unless you have some mathematical knoweldge unknown to the rest of mankind.
???? 3.59.9999999 is NOT equal to 4.00.
4.00 is equal to 4.00 - unless you have some mathematical knoweldge unknown to the rest of mankind.
So, I love this stuff. Yes, I have my BA in Mathematics and Statistics and I love this stuff. I really like placing myself on both sides of this argument - letting my mind completely accept the "real world" theory that .9bar can not be equal to 1 because they are different looking. I particularly like the "walk towards the door" argument - you will never get there even if you walk there infinitely, therefore the limit is the door, not the final outcome.
On the other side, I like the simplest explanation put forth - 1/3=.3bar, therefore 3*1/3=.3bar*3=1.
Now, my question for this discussion as a "real world" problem - is infinity proven or is still just a theory? One side will say yes, it exists, it goes on forever. The other side says no, and there is no way to prove it since life is finite. What if pi doesn't actually go on forever, it stops at some point, we just don't have the amount of time on earth to figure it out. There are no examples of infinity in real life and we will never find one since we are finite. If 1/3 is actually represented by an infinite line of 3's after the decimal point, how come 1/3 of an object is a finite amount? Therefore, as far as real seconds go, there cannot be an infinitely repeating 9 after a decimal point - it will equal 1. So, after the rambling, I guess it comes back to what a poster said a little while back, the OP is actually asking does 4:00=4:00, but writing it with a different terminology, it is semantics. 3:59.9bar doesn't exist - it is 4:00.
So the real question should be "is 3:59.9999.....to infinity minus one (for lack of a better way to put it) sub-4?"
captain apostrophe wrote:
???? 3.59.9999999 is NOT equal to 4.00.
4.00 is equal to 4.00 - unless you have some mathematical knoweldge unknown to the rest of mankind.
You are correct.
However, 3.59.999999... IS equal to 4.00.
3.59.99999... is equal to 4.00 because...
4.0 - x = 3.59.9999999... repeating
What is x?
x is 0.0000 repeating!
Please! Somebody make a ruling. I just ran a 3:59.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
Oops!,never mind. It wasn't a full mile. It was .99999999999999999999999999999999999999999999999999999 of a mile.
When time is expressed in seconds only the first 45 or so decimal points are physically meaningful. Beyond this you are talking about divisions of the Planck time, during which no motion occurs. So your physical state at 3:59.9bar is not different than your physical state at 4:00, regardless of whether you think these are the same or different numbers. If you have traveled at least 1 mile at 3:59.9bar, then you have definitely broken 4 min. I say at least 1 mile because in reality you have to travel a multiple of Planck distances, which may not divide evenly into 1 mile (a full mile).
This is all moot. It is impossible to run 3:599999 repeating. No watch has infinite decimal places. At some point, the nines stop repeating. And you are therefore under 4:00
Case closed
The sum of the series is necessarily 1, and you will always reach the door.
asfsadfasdfasdf wrote:
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.
If my watch battery dies, will I cease to be able to run in any time?If I run with a defective watch, can I finally break 4 minutes?
case closer wrote:
This is all moot. It is impossible to run 3:599999 repeating. No watch has infinite decimal places. At some point, the nines stop repeating. And you are therefore under 4:00
Case closed
asfsadfasdfasdf wrote:
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.
Actually, you will (provided that the time that it takes to make each successive step is half that of the previous step).
If I'm traveling at the speed of light and you run a mile, and your watch says 3:59.999999999....8 what does my watch say?
ehhhh wrote:What if pi doesn't actually go on forever, it stops at some point, we just don't have the amount of time on earth to figure it out.
Pi has been proven to have never ending, non-repeating decimal places.
really? Then where does it end? :)
Thank you leaping lanny, haha. I know there are "infinite terms" and all that, I understand there are proofs of these. I'm just saying in the real world does infinity exist? How can we ever know?
I knew I was going to get flamed for this - infinity is proven in mathematics. My question is about reality - how can you define "infinity", or better yet, say something is never ending without seeing the end? Do you understand where I am going with this? To solve a problem there must be an end - an answer. With infinity is there an end? By definition no, so how can we have a definitive answer? So does .3bar exist? I think it is used to express 1/3 (the more definite representation of the ratio). Does 3.14159265.... exist? I think the more definite representation is the ratio of Circumference/Diameter. Does .9bar exist? I think the better representation of the ratio is 1.
madmax wrote:
When time is expressed in seconds only the first 45 or so decimal points are physically meaningful. Beyond this you are talking about divisions of the Planck time, during which no motion occurs. So your physical state at 3:59.9bar is not different than your physical state at 4:00, regardless of whether you think these are the same or different numbers. If you have traveled at least 1 mile at 3:59.9bar, then you have definitely broken 4 min. I say at least 1 mile because in reality you have to travel a multiple of Planck distances, which may not divide evenly into 1 mile (a full mile).
Best post on this thread; everyone else is doing this faux-debate on complex math, and you take it to an even higher level of geekdom.
The best proof I've seen for proving .9999999 repeating equals 1:
Any two distinct numbers in a continuous set have an infinite number of distinct numbers between them.
If .99999999... != 1 then there is a distinct number x, such that x > .999999... and x .99999999999999...99999, a contradiction.
Having a Math degree I fully understand that 3:59.999...repeating = 4:00.
Those that don't get that may also think the Earth is flat.
But for the same reason, 4:00.00 = 3:59.99bar
I like the post that said if the first number you read is 3, then you ran sub 4.
Therefore if you run 4:00.00 you can argue that you ran sub 4.
I just blew my own mind!
I don't possess anything approaching the math skills to jump in here, but I do have a pretty strong finance background and I'd like to hear from the mathematics guys how you'd graphically represent 3.999repeating to = 4
I've been trying to think how to do it, and it seems impossible to graph them equally on either vertical or horizontal axis.
You put the 3.99999.. in the same place as the 4.