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 ?

WHAT IS A PARADOX ?

ZENO OF ELEA

Circa 490 BC-Circa 430 BC

Eleatic school of Parmenides

Inventor of dialectic

ACHILLE AND THE TORTOISE

NO CHANCE

A

B

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 ?

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 ............

WILL ACHILLE PASS THE TORTOISE?

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

1-2

1 __27

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 __64

THE DISTANCE BETWEEN ZAPPER AND THE CRUMB IS 1 M

WHAT IS THE SUM OF 3/4 +3/16 +

3/64 ............

3 __16

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?