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The newest challenge is the following:
As an example, we can easily go from ##0## to ##-1/3##. Indeed, we can apply ##T## to ##0## to go to ##1##, we apply ##T## to go to ##2##, we apply ##T## to go to ##3##, and then we apply ##R## to go to ##-1/3##.
Challenge:
Define the functions ##R(x)= -1/x## and ##T(x)=x+1##. Let ##q## and ##q^\prime## be two rational numbers. Prove that we can go from ##q## to ##q^\prime## in finitely many steps by applying ##T## and ##R## in a certain combination.
As an example, we can easily go from ##0## to ##-1/3##. Indeed, we can apply ##T## to ##0## to go to ##1##, we apply ##T## to go to ##2##, we apply ##T## to go to ##3##, and then we apply ##R## to go to ##-1/3##.
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