Maybe this might jog both your memories on definition of capitalism and classes-
"Capitalism
The socio-economic system where social relations are based on commodities for exchange, in particular private ownership of the means of production and on the exploitation of wage labour.
Wage labour is the labour process in capitalist society: the owners of the means of production (the bourgeoisie) buy the labour power of those who do not own the means of production (the proletariat), and use it to increase the value of their property (capital). In pre-capitalist societies, the labour of the producers was rendered to the ruling class by traditional obligations or sheer force, rather than as a “free” act of purchase and sale as in capitalist society.
Value is increased through the appropriation of surplus value from wage labour. In societies which produce beyond the necessary level of subsistence, there is a social surplus, i.e. people produce more than they need for immediate reproduction. In capitalism, surplus value is appropriated by the capitalist class by extending the working day beyond necessary labour time. That extra labour is used by the capitalist for profit; used in whatever ways they choose.
The main classes under capitalism are the proletariat (the sellers of labour power) and the bourgeoisie (the buyers of labour power). The value of every product is divided between wages and profit, and there is an irreconcilable class struggle over the division of this product.
Capitalism is one of a series of socio-economics systems, each of which are characterised by quite different class relations: tribal society, also referred to as “primitive communism” and feudalism. It is the breakdown of all traditional relationships, and the subordination of relations to the “cash nexus” which characterises capitalism. The transcendence of the class antgonisms of capitalism, replacing the domination of the market by planned, cooperative labour, leads to socialism and communism. "
Classes-
"Class
A group of people sharing common relations to labor and the means of production.
"In the process of production, human beings work not only upon nature, but also upon one another. They produce only by working together in a specified manner and reciprocally exchanging their activities. In order to produce, they enter into definite connections and relations to one another, and only within these social connections and relations does their influence upon nature operate – i.e., does production take place.
"These social relations between the producers, and the conditions under which they exchange their activities and share in the total act of production, will naturally vary according to the character of the means of production.
Karl Marx
Wage Labour and Capital
Chpt. 5: The Nature and Growth of Capital
The notion of class, as it is used by Marxists, differs radically from the notion of class as used in bourgeois social theory. According to modern capitalist thinking, class is an abstract universal defined by the common attributes of its members (i.e., all who make less than $20,000 a year constitute a "lower" class); categories and conceptions that have an existence prior to and independent of the people who make up the class.
For dialectical materialism however, the notion of class includes the development of collective consciousness in a class – arising from the material basis of having in common relations to the labour process and the means of production."
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www.marxists.org