WHAT IS A PARADOX ?.

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Presentation transcript:

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

WHAT IS A PARADOX ?

ZENO OF ELEA Circa 490 BC-Circa 430 BC Eleatic school of Parmenides Inventor of dialectic

ACHILLE AND THE TORTOISE HOW MANY POINTS THERE ARE IN A SEGMENT ? HOW BIG IS A POINT? WHAT IS THE SUM OF 100+10 +1+ 0,1 + 0,01 + 0,001 + 0,0001 ............ B WILL ACHILLE PASS THE TORTOISE? A THE TORTOISE START 100 M IN FRONT OF ACHILLE ACHILLE IS TEN TIME FASTER AS THE TORTOISE (if the tortoise run 10 m Achille will run 100 m) WHEN ACHILLE HAVE RUN 100 M WHERE IS THE TORTOISE ? NO CHANCE

ZAPPER AND THE SOFT PART OF THE BREAD 1-2 1-4 1-8 1 __16 THE DISTANCE BETWEEN ZAPPER AND THE CRUMB IS 1 M WHAT IS THE SUM OF 1/2 +1/4 + 1/8 + 1/16 +1/32 ............

ZAPPER AND THE SOFT PART OF THE BREAD 1-3 1-9 1 __27 1-2 THE DISTANCE BETWEEN ZAPPER AND THE CRUMB IS 1 M WHAT IS THE SUM OF 1/3 +1/9 + 1/27 + 1/81 ............

ZAPPER AND THE SOFT PART OF THE BREAD 2-3 2-9 2 __27 THE DISTANCE BETWEEN ZAPPER AND THE CRUMB IS 1 M WHAT IS THE SUM OF 2/3 +2/9 + 2/27+ 2/81 ............ CAN WE ANSWER THE PREVIOUS QUESTION?

ZAPPER AND THE SOFT PART OF THE BREAD 3-4 3 __16 3 __64 THE DISTANCE BETWEEN ZAPPER AND THE CRUMB IS 1 M WHAT IS THE SUM OF 3/4 +3/16 + 3/64 ............

SUMMARY

WILL ACHILLE REACH THE TORTOISE? ACHILLE'S SPEED: 14 M/S WHAT IS THE SUM OF 100+10 + 0,1 + 0,01 + 0,001 + 0,0001 ........?.. WHEN WILL ACHILLE PASS THE TORTOISE?