Is it possible for a country to support both freedom and equality?
I am of the opinion that freedom and equality are mutually exclusive. By nature, any attempts to enforce equality within a nation actively places restrictions on freedom and visa versa. For example if a business owner refuses to serve an individual, they are exercising their freedom to choose who they desire to serve, but by refusing to serve this individual, they have now created a situation where inequality is propagated because the individual who was refused service is no longer equal to his peers who still have access to service. On the flip side of this, If you create a law which forces the business to serve everyone equally, you have now infringed on the owner's freedom to choose who he wants to serve.
Another major problem can be observed in the very nature of what equality means. For an example, imagine two households with different incomes: one is very wealthy and lives in a huge mansion and the other is very poor and lives in a ghetto. Based on the differences in their incomes these two households are by no means equal. So how is this wage gap remedied so that both parties are on equal terms? If you were to give money to the poor household and bought them a mansion to live in they would be on equal terms with the wealthy household. But by giving only one of the households money, a new source of inequality is created, because if the system were truly equal, both households would be given equal amounts of money. In this respect, trying to create equality only propagates more inequality. The only way to create an equal system without transferring the burden of inequality is to restrict the freedoms of the individuals in a society. In this household example, that would be accomplished by creating a universal income which would restrict the individuals freedom to pursue wealth.
TL;DR- Because of the directly contradictory natures of freedom and equality, and the inherent ambiguity of what it means to be "equal" I believe that it is impossible for a country to support both freedom and equality.
What are your thoughts? Is there a way that these two ideas can coexist within a society? I'm curious to see what suggestions people come up with to contradict this.