# Return to Answer

 3 added 600 characters in body edited Jan 17 '15 at 22:56 Michael Lee 49011 gold badge33 silver badges1919 bronze badges (5 x 11111...)/(6 x 11111...) is not equal to 5/6 (5 x 11111...) equals infinity and (6 x 11111...) equals infinity. (infinity)/(infinity) is always undefined. The obscure nature of Pythagoras' School makes it hard to know who discovered irrational numbers (Hippasus?). They probably found the difficulty while examining a right triangle whose sides a and b are both equal to one. Perhaps, to their horror, they found the number two is not a perfect square (e.g. 4, 9, 16, ... are perfect squares and render an integer when their square root is taken). Pythagoras reasoned 'all is numbers' and also, that for any right triangle, the squares of sides a and b is exactly equal to the square of its hypotenuse (line c), but this can be said another way, the square erected on the diagonal of a square has twice the area of the original square. The difficulty they had was trying to create a ratio of two integers that would account for the square root of two. They tried and tried and tried, and they couldn't find such a ratio. Someone (Euclid?) later proved such a ratio does not exist. (The Presocratics, Philip Wheelwright (Editor), 1997, p.206). (5 x 11111...)/(6 x 11111...) is not equal to 5/6 (5 x 11111...) equals infinity and (6 x 11111...) equals infinity. (infinity)/(infinity) is always undefined. The obscure nature of Pythagoras' School makes it hard to know who discovered irrational numbers (Hippasus?). They probably found the difficulty while examining a right triangle whose sides a and b are both equal to one. Perhaps, to their horror, they found the number two is not a perfect square (e.g. 4, 9, 16, ... are perfect squares and render an integer when their square root is taken). (5 x 11111...)/(6 x 11111...) is not equal to 5/6 (5 x 11111...) equals infinity and (6 x 11111...) equals infinity. (infinity)/(infinity) is always undefined. The obscure nature of Pythagoras' School makes it hard to know who discovered irrational numbers (Hippasus?). They probably found the difficulty while examining a right triangle whose sides a and b are both equal to one. Perhaps, to their horror, they found the number two is not a perfect square (e.g. 4, 9, 16, ... are perfect squares and render an integer when their square root is taken). Pythagoras reasoned 'all is numbers' and also, that for any right triangle, the squares of sides a and b is exactly equal to the square of its hypotenuse (line c), but this can be said another way, the square erected on the diagonal of a square has twice the area of the original square. The difficulty they had was trying to create a ratio of two integers that would account for the square root of two. They tried and tried and tried, and they couldn't find such a ratio. Someone (Euclid?) later proved such a ratio does not exist. (The Presocratics, Philip Wheelwright (Editor), 1997, p.206). 2 added 412 characters in body edited Jan 17 '15 at 16:42 Michael Lee 49011 gold badge33 silver badges1919 bronze badges (5 x 11111...)/(6 x 11111...) is not equal to 5/6 (5 x 11111...) equals infinity and (6 x 11111...) equals infinity. (infinity)/(infinity) is always undefined. The obscure nature of Pythagoras' School makes it hard to know who discovered irrational numbers (Hippasus?). They probably found the difficulty while examining a right triangle whose sides a and b are both equal to one. Perhaps, to their horror, they found the number two is not a perfect square (e.g. 4, 9, 16, ... are perfect squares and render an integer when their square root is taken). (5 x 11111...)/(6 x 11111...) is not equal to 5/6 (5 x 11111...) equals infinity and (6 x 11111...) equals infinity. (infinity)/(infinity) is always undefined. (5 x 11111...)/(6 x 11111...) is not equal to 5/6 (5 x 11111...) equals infinity and (6 x 11111...) equals infinity. (infinity)/(infinity) is always undefined. The obscure nature of Pythagoras' School makes it hard to know who discovered irrational numbers (Hippasus?). They probably found the difficulty while examining a right triangle whose sides a and b are both equal to one. Perhaps, to their horror, they found the number two is not a perfect square (e.g. 4, 9, 16, ... are perfect squares and render an integer when their square root is taken). 1 answered Jan 17 '15 at 16:21 Michael Lee 49011 gold badge33 silver badges1919 bronze badges (5 x 11111...)/(6 x 11111...) is not equal to 5/6 (5 x 11111...) equals infinity and (6 x 11111...) equals infinity. (infinity)/(infinity) is always undefined.