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Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [22]
The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures.
The earliest form of mathematics was phenomenological. For example, if someone could draw a reasonable picture, or give a convincing description, then that met all the criteria for something to be described as a mathematical “fact”. On occasion, analogical arguments took place, or even by “invoking the gods”. The idea that mathematical ...
Such a proof is again a refutation by contradiction. A typical example is the proof of the proposition "there is no smallest positive rational number": assume there is a smallest positive rational number q and derive a contradiction by observing that q / 2 is even smaller than q and still positive.
Socratic questioning (or Socratic maieutics) [1] is an educational method named after Socrates that focuses on discovering answers by asking questions of students. According to Plato, Socrates believed that "the disciplined practice of thoughtful questioning enables the scholar/student to examine ideas and be able to determine the validity of those ideas". [2]
Image credits: anon #6. People really need to stop pretending like celebrities are the personas they portray on red carpets, in interviews etc. Most of the actors I’ve worked with are noticeably ...
The difference between self-imposed and world-imposed ethical dilemmas concerns the source of the conflicting requirements. In the self-imposed case, the agent is responsible for the conflict. [4] [2] A common example in this category is making two incompatible promises, [12] for example, to attend two events happening at distant places at the ...
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