Geometry
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Postulating in mathematics is simply stating stating or assuming something, usually an equation, to be true without having to prove it. This aids in the development of new mathematical theories. Commonly used postulates are Einsteins theories and his laws of the physics.
No. The field of mathematics pre-dates Einstein by at least 2000 years but he did use some very advanced mathematics to develop and quantify his theories.
Detectives have to prove their theories. Mathematics is one method of proving their case. Numbers don't lie.
No. If you work within its definitions and the rules of logic it is not flawed. There are mathematical statements that you cannot prove to be true or false (Godel's incompleteness theorem), but that is not a flaw.
Analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series and analysis functions.