Take any two non-equal numbers
Consider equation
Let
Thus, ALL POSITIVE NUMBERS ARE NEGATIVE!
Suppose
Let
Having had experience with some faulty proofs above, can you now answer the following questions
(a) From the equality
(b) For what value of
(1)
(c) If
We prove by mathematical induction that all horses in the world are of the same colour.
Base case: There is a single horse. It has some coat colour. Because there are no other horses, all the horses have the same coat colour.
Induction step: We have
The third step: due to mathematical induction rule, all the horses in the world have the same coat colour. THUS WE HAVE PROVED THAT ALL HORSES IN THE WORLD ARE OF THE SAME COLOUR!
You have 26 constants, labeled
Suppose you have a coffee mug made of stretchy and expandable material. How do you mold it into a donut that has a hole inside?