Is there a limit to the decimal expression .999?

[matt grime]

If we make a reasonable assumption about zeno's paradox, that both speeds are constant, then it just states that they will not meet before some fixed time (dependent on the ratio between the speeds). given that the observation that zeno's paradox does not stop you overtaking on the motorway, perhaps you ought to look at it and figure out where it's wrong for yourself, ram.

 

[ram1024]

If we make a reasonable assumption about zeno's paradox, that both speeds are constant, then it just states that they will not meet before some fixed time (dependent on the ratio between the speeds). given that the observation that zeno's paradox does not stop you overtaking on the motorway, perhaps you ought to look at it and figure out where it's wrong for yourself, ram.

Zeno's Observation is ABSOLUTELY correct. the conclusion he came to is incorrect because of the times he was living in this was a relatively unexplored field.

Tell me where I'm wrong in saying you will NEVER reach 1 in this series outlined in this problem

Object A traveling From Point B to Point C which is a measured distance of 10 meters, and moving at a speed of 10 meters per second.

Object A must first travel 1/2 the distance (5 meters) then 1/2 the remaining distance (2.5 meters) then 1/2 that remaining distance (1.25 meters) etc ad infinitum.

the series has a LIMIT of 10 meters, but the SUM of the series will NEVER be 10 meters. there will ALWAYS be some portion "half distance" left over to travel, infinitely small and beyond human comprehension.

SOMETHING cut into 2 parts will ALWAYS yield SOMETHING. 1/Infinity ≠ 0

 

[Integral]

A number inclusive in the set that is comprised of numbers less than infinity and greater than negative-infinity

This is pretty funny. Clearly all that you know about the real number line can be written on a decimal point.
The world of mathematicans defines Infinity as an addition to the Real Number line. In doing so the field nature of the Real numbers is lost. In reality Infinity is not a number, but a definition, part of the definition is how Infinity behaves under each of the operations. It is by DEFINITION that

$$\frac 1 {\infty} = 0$$

no i said an infinite number of half-distances will NOT reach a destination

But Since that is a convergernt series, Math says that it DOES reach the end after an infinite number of steps.

 

[Integral]

http://home.comcast.net/~rossgr1/Math/one.PDF

I have a sneaking suspicion that you simply do not have enough mathematical sophistication to understand formal proofs, so I doubt that the above link will be meaningful. If you can get yourself out of the lecturing mode into the learning mode you may actually be able to get a glimmer of how mathematic ans look at this problem. In this thread you are arguing with at least one Mathematics PhD and several graduate level math students. Given acess to this level of knowledge it is a shame that you cannot make some effort to learn something.

 

[ram1024]

This is pretty funny. Clearly all that you know about the real number line can be written on a decimal point.
The world of mathematicans defines Infinity as an addition to the Real Number line. In doing so the field nature of the Real numbers is lost. In reality Infinity is not a number, but a definition, part of the definition is how Infinity behaves under each of the operations. It is by DEFINITION that

$$\frac 1 {\infty} = 0$$

well that definition is CLEARLY wrong then. I don't know why you guys are using "an infinity" that has clear limits as such, but it's ridiculous.

it's a good thing you guys live in seclusion and never come out to see the real world, because in the real world, something is never nothing, not matter how you cut it.

find me the guy that invented your infinity cause i wish to verbally abuse him.

 

[Hurkyl]

Anyways, seeing how everyone participating here other than ram1024 is in agreement on the subject, and ram1024 has rejected all arguments in advance, I see no further point for this thread.