The discussion centers on establishing the equivalence of three mathematical statements as presented in the book "Formal Proofs in Maths." The statements include the inequalities \(0 < 1\), \(0 < A \Rightarrow 0 < \frac{1}{A}\), and the condition \(AC < BC \wedge 0 < C \Rightarrow A < B\). Participants express the need for a solution to exercise 19 on page 101, highlighting the lack of provided answers in the text. The conversation concludes with the acknowledgment that this remains an unsolved challenge question.
PREREQUISITESMathematicians, educators, students studying formal proofs, and anyone interested in deepening their understanding of mathematical equivalences and inequalities.
solakis said:From the book "FORMAL PROOFS IN MATHS "(Amazon.com),page 101 ,exercise19 ,Iread:
Establish the equivalence between:
$$0<1$$,.........$$0<A\Longrightarrow 0<\frac{1}{A}$$,............$$AC<BC\wedge 0<C\Longrightarrow A<B$$
MarkFL said:Please post the solution you have ready.