Redox reactions between metals and nonmetals typically involve a complete transfer of electrons to form ionic compounds; hence, they are easy to identify. However, redox reactions involving only nonmetals with a partial transfer of electrons are not as easily identifiable. 

Redox reactions are characterized by changes in the oxidation states of the atoms, which indicates electron movement between the atoms.

The oxidation state, or oxidation number, of an atom in a compound is the charge it would have if the shared electrons in each heteronuclear bond were completely transferred to the more electronegative atom. Homonuclear bonds are divided equally.

For instance, in gaseous hydrogen chloride, chlorine is more electronegative. If hydrogen’s electron is transferred completely to chlorine, chlorine gets a 1− charge, corresponding to the −1 oxidation state, and hydrogen gets a 1+ charge, corresponding to the +1 oxidation state.

Oxidation states can be assigned to atoms in elemental form and in most ions and compounds using specific rules. The first three rules are always followed. The remaining rules are applied one by one until the first three rules are satisfied. 

These rules will now be applied to identify whether the formation reactions of sulfur dioxide and calcium carbonate are redox reactions.

According to rule number 1, elements in the free state have an oxidation number of zero, so elemental sulfur and oxygen are both assigned the oxidation number zero.

According to rule number 3, the sum of the oxidation numbers in a neutral compound is zero so the oxidation numbers of sulfur and oxygen in SO₂ must sum to zero.

In accordance with rule number 6, the oxidation number of each oxygen is −2 in SO₂. Two oxygen atoms sum to −4. The oxidation number of sulfur is, therefore, +4.

The oxidation number of sulfur increases from zero to +4, so it is oxidized, while the oxidation number of oxygen decreases from zero to −2, so it is reduced. Thus, this is a redox reaction.

In the case of calcium carbonate, the oxidation number of oxygen is −2 in all three compounds, and calcium is +2 in calcium oxide and calcium carbonate. According to rule 3, carbon must be +4 in carbon dioxide and calcium carbonate.

Since there is no change in the oxidation numbers of the atoms during the reaction, this is not a redox reaction.