A reduction decreases an oxidation state, recording gain in the formal electron assignment. For , the decrease is . The reduced chemical species serves as the oxidizing agent in the coupled redox.[ref]
Chemistry 2e by Paul Flowers and others. §4.2, “Oxidation-Reduction Reactions”: reduction as decreasing oxidation number
In the electrochemistry examples here, reduction is gain of electrons by a chemical species; it occurs at the cathode. That electrode definition holds in both a galvanic cell and an electrolytic cell; it does not fix terminal polarity.
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