Why a Mathematician can’t travel 1 mile even in infinite time?

Can you believe a mathematician can’t complete 1 mile distance even after taking infinite time. It’s very interesting to know, after all why does this happen?

When you think practically, it seems like humor. As you all know mathematics is very interesting subject. That all, which is practically possible in this world, is also possible in mathematics and which is  impossible practically, is possible in mathematics.

To understand paradox mentioned above, lets consider an example.

Suppose there is a boy named John who wants to travel 1 mile. Now you would be thinking is there any rocket science in travelling 1 mile distance? You are right, of course there is no rocket science.

Then why, John can’t travel 1 mile even in infinite time?

Before travelling, there is a condition which must have to be fulfilled by John.

Condition is as follows

Suppose John is at point A, which is 0 and he wants to go at point B, which is 1. First time john must have to travel half of the total distance. Besides this, he must have to always travel half of the remaining distance.

Mathematically you can understand this as:

John has been given distance of 1 mile. According to condition, John must have to travel half of the distance.

So, distance travelled by john in first time would be

 

               Total distance / 2 = 1 / 2 = 0.5 mile

Now consider second condition: John must have to always travel half of the remaining distance.  

So,

 Remaining distance = total distance - travelled distance

                                      =   1 – 0.5

                                      =    0.5 mile

Now distance travelled by John in second time would be

                         Remaining distance/ 2 = 0.5 / 2 = 0.25 mile

So,

 Remaining distance = total distance - total travelled distance

                                  = 1 – ( 0.5 + 0.25)

                                  = 1- ( 0.75)

                                  =  0.25 mile

 Now John would travel in third time

                       Remaining distance / 2 =  0.25 / 2 = 0.125 mile

So,

Remaining distance = total distance - total travelled distance

                                    = 1 – ( 0.5 + 0.25 + 0.125 )

                                   =  1 – ( 0.875)

                                   =  0.125 mile

Now John would travel in fourth time

             Remaining distance / 2 = 0.125 / 2 = 0.0625 mile

So,

 Remaining distance = total distance – total travelled distance

                                     = 1 – ( 0.5 + 0.25 + 0.125 + 0.0625 )

                                     = 1 – ( 0.9375 )

                                     =  0.0625 mile 

Now John would travel in fifth time

                 Remaining distance / 2 = 0.0625 / 2 = 0.03125 mile

So,

Remaining distant = total distance - total travelled distance

                             = 1 – ( 0.5 + 0.25 + 0.125 + 0.0625 + 0.03125 )

                             = 1 – ( 0.96875 )

                             = 0.03125 mile

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Continue in this way, on and on.

 

Now, lets see how much distance John has travelled so far  

 

John travelled total distance in 1^st time = 0.5 mile

John travelled total distance in 2^nd time = 0.75 mile

John travelled total distance in 3^rd time = 0.875 mile

John travelled total distance in 4^th time = 0.93755 mile

John travelled total distance in 5^th time = 0.96875 mile

John travelled total distance in 6^th time = 0.984375 mile

John travelled total distance in 7^th time = 0.9921875 mile

John travelled total distance in 8^th time = 0.99609375 mile

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After continuing in this way you can see John is not reaching exactly at B, although he is reaching approximately at B.