The discussion revolves around proving the inequality a/b < (a+1)/(b+1) under the condition that b is a positive number and a < b. Participants are exploring various methods to approach this proof.
There is an ongoing exploration of different approaches to the problem. Some participants have offered suggestions, such as adding terms to both sides of the inequality, while others reflect on their previous attempts and errors.
Participants are working under the assumption that b is positive and that a is less than b, which is central to the inequality being discussed. There is acknowledgment of mistakes made in earlier attempts, which may affect the direction of the discussion.
John H said:Homework Statement
Prove that if b is a positive number, such that a < b, then
a/b<(a+1)/(b+1)
2. The attempt at a solution
I have tried a few things, attempting to prove it using the real line, and a bunch of other methods but have had no success. I Would greatly appreciate it if u can at least get me started.