We define two numerical operations labeled 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 2 we obtain – ½, and 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 into 2/5 by successively applying the operations T, T, T, R, T, T, R, T:
0 ---T ---> 1 ---T---> 2 ---T ---> 3 ---R---> -1/3 ---T ---> 2/3 ---T ---> 5/3 ---R ---> -3/5 ---T ---> 2/5.
Explain how 0 can be turned into any negative integer.
start with 0 then add T, one more T, and after that you can do anything you wish, as long as you have an odd number of R operations. Check my thinking.
To turn 0 into any negative integer, we can use the operations T and R in a specific sequence.
First, we apply the operation R to 0. However, since R cannot be applied to 0, we need to convert 0 into a non-zero number. We can achieve this by applying the operation T multiple times. Each time we apply the operation T to 0, the number increases by 1.
Once we have a non-zero number, we can then apply the operation R to find the negative reciprocal. For example, if we apply the operation T four times to 0, we obtain 4. Then, by applying the operation R, we find the negative reciprocal of 4, which is -1/4.
In general, to turn 0 into any negative integer, we need to perform the following steps:
1. Apply the operation T multiple times to convert 0 into a non-zero number.
2. Apply the operation R to find the negative reciprocal of the non-zero number obtained in step 1.
By repeating these steps, we can turn 0 into any negative integer. However, it is important to note that R can never be applied to 0 itself.