There is 1 number can't written like that. The number is 0.
So the statement is wrong.

jasen's post in Gime a Clue was marked as the answer
November 4, 2015

jasen's post in SBT Fraction was marked as the answer
October 21, 2015

modified Stern-Brocot Tree to third sequence. 3rd sequence 34/55 157/254 123/199 212/343 89/144 233/377 144/233 199/322 55/89 since it use fibbonaci number, which is relatively prime, so the fraction is already in simple form. so there is no fraction with 55<b<89

after a week long journey abroad, now I'm active again.

After thinking again, and using the clue harrey give us (scisors, pen, and paper), Yes it is possible to prove it without computer, but it takes many steps.

jasen's post in Number was marked as the answer
October 2, 2015