a number wrote:
You put the 3.99999.. in the same place as the 4.
By that logic I could make 3 = 46
I'm not saying 3.999 repeating does not equal 4, but I'd like to see it drawn. If there is a line with a height of 4, I can't see how a line with a length of 3.anything ever reaches it.
I don't know why I care so much. I don't understand the underlying theory, but I assumed I could chart anything.
Can you chart everything or just some easy numbers? How do you chart the cube root of 2.
Voice of Ray-san wrote:
If my watch battery dies, will I cease to be able to run in any time?
No you will cease to be able to record it
If I run with a defective watch, can I finally break 4 minutes?
No, you will still be a moron.
a number wrote:
Can you chart everything or just some easy numbers? How do you chart the cube root of 2.
Brah, not helpful. I admitted I don't understand the underlying math, and I'm trying to get a picture of it.
I assume someone can actually help me. I am curious.
If you dont know how to a draw line with whatever length you want then there is nothing to understand. 3.999999.. is the same length as 4 because that is the rule.
If you do in fact finish the race, then the time on the watch can not extend infinitely. Can it? Since you crossed the line and stopped, doesn't the line of .9s also have to stop?
skinny texan wrote:
If you do in fact finish the race, then the time on the watch can not extend infinitely. Can it? Since you crossed the line and stopped, doesn't the line of .9s also have to stop?
See THIS is a good example of a representation how graphing this seems impossible.
You have to stop SOMEWHERE before a distance (or time) of 4 is hit. I don't see how it can be equivalent in practice. Theory says a lot, but the world exists in a certain state.
Which is why finance guys make a lot more than mathematicians!
If you take 3.99999.. and stop it off after a while and use 3 with a certain number of 9's after the decimal point then that is not the same as 3.9999.. going on forever.
dude no you wont.. if each step you take is half the distance to the door you will never hit it. its an assymptote.
1, 1/2, 1/4, 1/8, 1/16, 1/32.... so you can say your term is 1/2^n with n=0. does that work out to be a telescoping series? regardless, in reality you wont hit the door and the door is the limit
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?
No, but you get close enough to reach out with your arm and open the door :)
the computer might not give it to you but if you have FAT timed it and the picture shows your torso crossing the line before 4:00, I think you should be called a sub-4:00 miler, even if your time rounds up to 4:00.00
If that were true, no one could ever leave a room with a door.
asfsadfasdfasdf wrote:
dude no you wont.. if each step you take is half the distance to the door you will never hit it. its an assymptote.
1, 1/2, 1/4, 1/8, 1/16, 1/32.... so you can say your term is 1/2^n with n=0. does that work out to be a telescoping series? regardless, in reality you wont hit the door and the door is the limit
Maybe a better way to look at it is to try and quantify the magnitude of the difference between 1 and 0.999...
If I use fractions to express dividing 1 by 3, and then multiplying by 3, I end up with (1/3) * 3 = 3/3 = 1.
If I use decimals to express dividing 1 by 3, and then multiplying by 3, 1 end up with (0.333...) * 3 = 0.999...
What's the difference between the two results? (Hint: 0) How can the same mathematical operations produce two different results simply by using a different notation?
For any positive number you can think of, the difference between 1 and 0.999... will always be less than that number. Only 0 (or any negative number) is less than any arbitrary positive number.
Voice of Ray-san wrote:
Maybe a better way to look at it is to try and quantify the magnitude of the difference between 1 and 0.999...
Maybe not.
Sounds like the kind of tactics Brandon Moen would use....
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.
no way 3:59.999999... is not breaking 4, it is the quivalent of 4:00.00
The original question is pretty stupid, since there is no physical way for time to be measured to an infinite series of decimals. Every measuring device ever made by man counts up by a certain increment, and there is inevitably some space between those increments. .9 repeating would fall into the space between .9999 (to however many digits are measured) and 1.
And yes, .9 repeating does in fact equal 1. It's hard to understand, so you sort of just have to take it as being true. One way to think about this is that there is no value, however small, that can be added to .9 repeating to give you 1. Thus, the two must be the same. Or, if you need a proof:
x=.99999999999999...
10x=9.99999999999...
10x-x=9.9999.... - .999999....
9x=9
x=1
Really, you have to take a step back and think of it as being a value, with a set place on the number line. That value cannot be getting closer and closer to 1, it has a set position. If you try to mark it down as .9999999 or even .9999999999999, its not there. There are no numbers on the number line betweent .9 repeating and 1, so the two must therefore be equal.
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.
The point is that it is not faster. It is exactly the same. You're really just writing the same number two different ways and claiming that one is faster than the other. It's like arguing that high jumping 6 and 1/2 feet is better than high jumping 5 and 3/2 feet.
If you disagree, you can prove us all wrong quite easily by naming a number between .999(repeating) and 1.