Abstract
This article presents a cardinality approach to big data, a fuzzy logicbased approach to big data, a similarity-based approach to big data, and a logical approach to the marketing strategy of social networking services. All these together constitute a mathematical theory of big data. This article also examines databases with infinite attributes. The research results reveal that relativity and infinity are two characteristics of big data. The relativity of big data is based on the theory of fuzzy sets. The relativity of big data leads to the continuum from small data to big data, big data-driven small data analytics to become statistical significance. The infinity of big data is based on the calculus and cardinality theory. The infinity of big data leads to the infinite similarity of big data. The proposed theory in this article might facilitate the mathematical research and development of big data, big data analytics, big data computing, and data science with applications in intelligent business analytics and business intelligence.
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