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When things burn, they are just rapidly oxidising, so the Magnesium, since it is highly reactive, can ignite without any external fuels, or without it being in a compound. The reaction for this oxidisation is: 2 Mg + O2 = 2MgO. The reason we use 2 magnesium atoms, is because the oxygen in the air is, like the majority of elemental gases, is found in the elemental form.

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