SOME PHILOSOPHICAL/MATHEMATICAL CONUNDRUM

   1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + ... TENDS TO BE EQUAL TO 1

BUT SINCE THE SEQUENCE IS INFINITE, THERE ALWAYS BE A SMALLER NUMBER PREVENTING FROM EQUALLING TO 1!

HOWEVER:

TAKE AN EXISTING SQUARE:

SINCE THIS SQUARE IS OF EXISTENCE, IT COULD BE DEFINED BY A NUMBER (one representing a surface - in square meter for instance). LET'S TAKE 1 FOR THIS REPRESENTATIVE NUMBER!

THE SQUARE CAN BE DIVISED IN HALF. ONE OF THE TWO HALVES CAN ALSO BE DIVISED IN HALF. ONE OF THE NEW HALF ALSO CAN IN TURN BE DIVISED IN HALF.

AND SO ON, INDEFINITELY.

WE'LL FIND ALWAYS A NEW HALF SINCE THIS SEQUENCE IS INFINITE.

THERE'LL ALWAYS BE A NEW HALF PREVENTING FROM COMPLETING THE SQUARE.

THEREFORE 1 SHOULD NEVER BE REACHED!

AND YET THE SQUARE EXISTS! 1 IS WELL AND TRULY A TANGIBLE REALITY THAT EVERYBODY CAN SEE FOR ONESELF AND THAT MATHEMATICS CANNOT REACH.

HOW ABOUT THAT!