$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or. . . .

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

Keep constructing triangles in the incircle of the previous triangle. What happens?

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

If a sum invested gains 10% each year how long before it has doubled its value?