cover -- copyright page -- title page -- Contents -- Introduction -- Acknowledgments -- I Paradoxes -- Functions and Limits -- Laying bricks -- Spiral curves -- A paradoxical fractal curve: the Koch snowflake -- A tricky fractal area: the Sierpinski carpet -- A mysterious fractal set: the Cantor ternary set -- A misleading sequence -- Remarkable symmetry -- Rolling a barrel -- A cat on a ladder -- Sailing -- Encircling the Earth -- A tricky equation -- A snail on a rubber rope -- Derivatives and Integrals -- An alternative product rule -- Missing information? -- A paint shortage -- Racing marbles -- A paradoxical pair of functions -- An unruly function -- Jagged peaks galore -- Another paradoxical pair of functions -- II Sophisms -- Functions and Limits -- Evaluation of lim_n _k=1n1n2+k proves that 1=0. -- Evaluation of lim_x0 (xsin1x ) proves that 1 = 0. -- Evaluation of lim_x0+ (xx) shows that 1 = 0. -- Evaluation of lim_n [n]n demonstrates that 1=. -- Trigonometric limits prove that sinkx = k sinx. -- Evaluation of a limit of a sum proves that 1=0. -- Analysis of the function x+yx-y proves that 1 = -1. -- Analysis of the function ax+yx+ay proves that a = 1a, for any value a 0. -- One-to-one correspondences imply that 1 = 2. -- Aristotle's wheel implies that R = r. -- Logarithmic inequalities show 2 > 3. -- Analysis of the logarithm function implies 2 > 3. -- Analysis of the logarithm function proves 14 > 12. -- Limit of perimeter curves shows that 2 = 1. -- Limit of perimeter curves shows = 2. -- Serret's surface area definition proves that = . -- Achilles and the tortoise -- Reasonable estimations lead to 1,000,000 2,000,000. -- Properties of square roots prove 1 = -1. -- Analysis of square roots shows that 2=-2. -- Properties of exponents show that 3 = -3. -- A slant asymptote proves that 2 = 1.

Euler's interpretation of series shows 12 = 1-1+1-1+@let@token . -- Euler's manipulation of series proves -1>>1. -- A continuous function with a jump discontinuity -- Evaluation of Taylor series proves ln2=0. -- Derivatives and Integrals -- Trigonometric integration shows 1 = C, for any real number C. -- Integration by parts demonstrates 1 = 0. -- Division by zero is possible. -- Integration proves sin2 x = 1 for any value of x. -- The u-substitution method shows that 2 < 0 < . -- ln2 is not defined. -- is not defined. -- Properties of indefinite integrals show 0=C, for any real number C. -- Volumes of solids of revolution demonstrate that 1 = 2. -- An infinitely fast fall -- A positive number equals a negative number. -- The power rule for differentiation proves that 2=1. -- III Solutions to Paradoxes -- Functions and Limits -- Laying bricks -- Spiral curves -- A paradoxical fractal curve: the Koch snowflake. -- A tricky fractal area: the Sierpinski carpet -- A mysterious fractal set: the Cantor ternary set -- A misleading sequence -- Remarkable symmetry: Reuleaux polygons -- Rolling a barrel -- A cat on a ladder -- Sailing -- Encircling the Earth -- A tricky equation -- A snail on a rubber rope -- Derivatives and Integrals -- An alternative product rule -- Missing information? -- A paint shortage -- Racing marbles -- A paradoxical pair of functions -- An unruly function -- Jagged peaks galore -- Another paradoxical pair of functions -- IV Solutions to Sophisms -- Functions and Limits -- Evaluation of lim_n n_k=1 1n2+k proves that 1 = 0. -- Evaluation of lim_x 0 ( xsin1x ) proves that 1 = 0. -- Evaluation of lim_x 0+ (xx) shows that 1 = 0. -- Evaluation of lim_n [n]n demonstrates that 1 = . -- Trigonometric limits prove that sinkx = ksinx. -- Evaluation of a limit of a sum proves that 1 = 0. -- Analysis of the function x + yx - y proves that 1 = -1.

Analysis of the function ax + yx + ay proves that a = 1a, for any value a 0. -- One-to-one correspondences imply that 1 = 2. -- Aristotle's wheel implies that R = r. -- Logarithmic inequalities show 2 > 3. -- Analysis of the logarithm function implies 2 > 3. -- Analysis of the logarithm function proves 14 > 12. -- Limit of perimeter curves shows that 2 = 1. -- Limit of perimeter curves shows = 2. -- Serret's surface area definition proves that = . -- Achilles and the tortoise -- Reasonable estimations lead to 1,000,000 2,000,000. -- Properties of square roots prove 1 = -1. -- Analysis of square roots shows that 2 = -2. -- Properties of exponents show that 3=-3. -- A slant asymptote proves that 2=1. -- Euler's interpretation of series shows 12 = 1-1+1-1+@let@token . -- Euler's manipulation of series proves -1>>1. -- A continuous function with a jump discontinuity. -- Evaluation of Taylor series proves ln2=0. -- Derivatives and Integrals -- Trigonometric Integration shows 1 = C, for any real number C. -- Integration by parts demonstrates 1 = 0. -- Division by zero is possible. -- Integration proves sin2 x = 1 for any value of x. -- The u-substitution method shows that 2 < 0 < . -- ln2 is not defined. -- is not defined. -- Properties of indefinite integrals show 0 = C, for any real number C. -- Volumes of solids of revolution demonstrate that 1 = 2. -- An infinitely fast fall -- A positive number equals a negative number. -- The power rule for differentiation proves that 2=1. -- Bibliography -- About the Authors.