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Maths and Nature

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What is Mathematics?

Mathematics was developed about 5,000 years ago by the Sumerians. They did this at the same time as they developed reading and writing. However, the roots of mathematics go back much more than 5,000 years. Throughout their history, humans have faced the need to measure and communicate about time, quantity, and distance and mathematics is an aiding tool to achieve this. Mathematics has been a part of the human search for understanding. Mathematical discoveries have come both from the attempt to describe the natural world and from the desire to arrive at a form of inescapable truth from careful reasoning. These remain fruitful and important motivations for mathematical thinking, but in the last century mathematics has been successfully applied to many other aspects of the human world: voting trends in politics, the dating of ancient artifacts, the analysis of automobile traffic patterns, and long-term strategies for the sustainable harvest of deciduous forests, ...

Symbols in Set theory

Table of set theory symbols: Symbol Symbol Name Meaning / definition Example { } set a collection of elements A={3,7,9,14}, B={9,14,28} A ∩ B intersection objects that belong to set A and set B A ∩ B = {9,14} A ∪ B union objects that belong to set A or set B A ∪ B = {3,7,9,14,28} A ⊆ B subset subset has fewer elements or equal to the set {9,14,28} ⊆ {9,14,28} A ⊂ B proper subset / strict subset subset has fewer elements than the set {9,14} ⊂ {9,14,28} A ⊄ B not subset left set not a subset of right set {9,66} ⊄ {9,14,28} A ⊇ B superset set A has more elements or equal to the set B {9,14,28} ⊇ {9,14,28} A ⊃ B proper superset / strict superset set A has more elem...

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