The proliferation of mathematics cranks on the Internet

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SUMMARY

The discussion highlights the prevalence of individuals on the Internet who hold incorrect beliefs about fundamental mathematical concepts, such as the equality of 0.999... and 1, and the existence of natural versus fractional numbers. These beliefs often stem from a misunderstanding of mathematical definitions and logical reasoning. The conversation suggests that the way mathematics is taught in schools may contribute to this confusion, as many individuals resist conventional mathematical wisdom despite its correctness. Effective education requires engagement from both teachers and students to foster understanding.

PREREQUISITES
  • Understanding of basic mathematical concepts, including real numbers and their properties.
  • Familiarity with mathematical logic and definitions.
  • Knowledge of constructivism in mathematics.
  • Awareness of common misconceptions in mathematics education.
NEXT STEPS
  • Research the concept of mathematical infinity and its implications on numbers like 0.999...
  • Explore the principles of constructivism in mathematics and its critiques.
  • Study effective teaching strategies for mathematics to enhance student engagement.
  • Investigate common mathematical misconceptions and how to address them in educational settings.
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Mathematics educators, curriculum developers, and anyone interested in improving mathematical understanding and addressing misconceptions in learning environments.

Gigasoft
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I've noticed on other discussion boards, that there is a surprisingly high number of people sharing a set of similar, unshakeable beliefs that contradict basic thereoms in mathematics and logic. Usually, these include:

- 0.999... not being equal to 1, or not existing
- That natural numbers exist, while fractional numbers don't
- The possibility that the definition of something can be untrue
- The belief that they have "proved" constructivism
- That you can start with a physical observation and conclude with a mathematical theorem

Does this indicate that there is something wrong with the way mathematics is introduced in schools, leaving people confused about mathematical and logical concepts and how they are defined? It's interesting that no attempt at explaining why they're wrong, gets through.
 
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Education is a two way street. If students aren't interested, it is hard for them to learn. Also there are a lot of people who like to disagree with "conventional wisdom", even if it correct. This applies to a lot of other areas besides mathematics.
 

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