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$2\wedge 3\wedge 4$ 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 $(r^r)^r$, where $r$ is $\sqrt{2}$?

# It's Only a Minus Sign

##### Age 16 to 18 Challenge Level:

The key for this problem is for students to appreciate that the signs in differential equations are of crucial importance in determining the structure of a solution. They can make the difference between solutions growing to infinity, oscillating or settling down to zero.

When constructing differential equations using, for example, $F \; = \; ma$, negative signs on the right hand side correspond to 'repulsions' and positive signs correspond to 'attractions'.

Understanding the structure of equations in this way is a very powerful approach which can transcend the details of the algebraic solution.