 There are important precursors of reverse mathematics. Weyl (1918) started to develop analysis using a minimalist foundation (that equates to \(\ACA_0\)) whilst Hilbert and Bernays (1939) developed analysis in second order arithmetic, whereby on closer inspection one sees that all they used is \((\bPi^1_1\Hy\bCA)_0\). The first theorem of genuinely reverse mathematics was established by Dedekind in his essay Stetigkeit und irrationale Zahlen (1872). It states that his continuity (or completeness) principle is equivalent to a well-known theorem of analysis, namely, every bounded, monotonically increasing sequence has a limit. He emphasizes, 