We define two numerical operations labelled T and R.
The effect of T is to add 1 to a number. For example, if we apply the operation T to the number 2 three times in a row, we obtain 3, then 4, then 5.
The effect of R is to find the negative reciprocal of a number. For example, if we apply the operation R to -3/2 we obtain 2/3. Note that R can never be applied to the number 0.
The operations T and R can be combined. For example, we can turn 0 in to 2/5 by successively applying the operations T, T, T, R, T, T, R, T.
a) Starting with 2, list the numbers produced by successively applying the operations T, R, R, T, R, T, R, T, R.
b) Find a sequence of operations which turns 3/4 into 2/3.
c) Find a sequence of operations which turns 3 into 0.
d) Find a sequence of 20 operations that turns 7 into 0.
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