Thread: zenos dichotomy applyed to 1/3 *3

all right a turtle wants to reach a destination one meter away:

first it makes a nineth of the way, then it makes a nineth of whats left and keeps doing a ninenth of whats left forever

will it arrive its destination?

no since in other words shell always be one tenth short of finish line

this proves 0.999... is not equal to 1

or would you say a turtle waking 0.1 of whats left forever will reach destination as well

The point that people keep missing for this kind of paradox is that the time intervals are proportional to the length intervals.

Originally Posted by luxtpm

all right a turtle wants to reach a destination one meter away:

first it makes a nineth of the way, then it makes a nineth of whats left and keeps doing a ninenth of whats left forever

will it arrive its destination?

no since in other words shell always be one tenth short of finish line

this proves 0.999... is not equal to 1

No, it proves that 0.99...9 does not equal 1, which is a completely different proposition.

A simple demonstration that 0.999... equals 1.

1/3 = 0.333...

3 x 0.333... = 0.999...

3 x 1/3 = 3/3 = 1

ergo,

0.999... = 1

Originally Posted by luxtpm

all right a turtle wants to reach a destination one meter away:

first it makes a nineth of the way, then it makes a nineth of whats left and keeps doing a ninenth of whats left forever

will it arrive its destination?

no since in other words shell always be one tenth short of finish line

this proves 0.999... is not equal to 1

or would you say a turtle waking 0.1 of whats left forever will reach destination as well

It seems you mixed two different Zeno’s aporias: "Achilles and turtle" and "the Arrow".
So in your post there isn’t any dichotomy – if you want for the turtle to reach a destination one meter through "1/9 (or 1/3-?) of full length steps" then you can consider at once the length equal to 9 meters and obtain that the turtle reached 1 meter without problem.

In the case of "Achilles and turtle" race – indeed, the distance between the competitioners sequentially decreases to the lim = zero, at that indeed "the time intervals are proportional to the length intervals". But both intervals never become be equal zero exactly (corresponding semantic is "there is no time/ space interval [at all]"; as well as 0.9999… isn’t exactly" equal to 1) - Achilles always will be behind a turtle. So to left the turtle behind is necessary for Achilles and turtle coordinates be uncertain, as that we know from QM.

An corresponding offtopic here. In the SSDZ post in the "1/0" thread is pointed out that the information in the set "Information" can propagate instantly, when in the arXiv links is pointed out that the time interval for cause-effect events cannot be equal zero. There isn’t a contradiction – the time interval can be infinitesimal, but that isn’t zero.

Cheers

That post made no sense.

0.999... (infinitely many 9s) is exactly equal to 1, and Achilles will pass the turtle.

(And posting about yourself in the third person makes you sound really strange. :?)