The formula C₂O₄ is incorrect. It should be either C₂O₄²⁻, the oxalate ion, or C₂O₄, which would be a neutral molecule that is not commonly observed.

Assuming you meant C₂O₄²⁻ (oxalate ion):

Here's how to determine the oxidation number of carbon in C₂O₄²⁻:

1. Assign known oxidation numbers: Oxygen usually has an oxidation number of -2.

2. Set up an equation: Let "x" represent the oxidation number of carbon. Since there are two carbon atoms, the equation becomes: 2x + 4(-2) = -2

3. Solve for x: 2x - 8 = -2

2x = 6

x = +3

Therefore, the oxidation number of carbon in the oxalate ion (C₂O₄²⁻) is +3.