Let me put this very simply, say we have a nation of people, nobody has anything, they are all equal.
0 = 0 = 0 = 0 = 0
then, we give them an equal share, every one gets 100 units of currency.
100 = 100 = 100 = 100 = 100
Now, if you enjoy your math, like I do, this equation is basically unchanged, and are essentially equal to each other.
That isn't true, because the value of money, like the value of everything else, is subjective. Each person may have the same amount of money, but that does not make them equally wealthy, and it is wealth, not currency, which is you are fundamentally trying to equalize.
The root economic cause of most wealth inequality is simply that some people choose to save and invest, while others choose to consume and live paycheck-to-paycheck. No amount of redistribution will bring about equal outcomes in the face of unequal preferences and goals. To make people truly equal you would have to take away their freedom to choose.