An Investigation to Continuum Hypothesis

Lam, Kai S

doi:10.2139/ssrn.3181915

Cited by 1 publication

(2 citation statements)

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“…The ancient Greeks believed that actual infinity was not a process in time, rather, it was an infinity that existed at any time (it had an infinite amount of elements). Specifically, the process of potential infinity is infinite but its value is finite at any specific time 1 (it contains many finite elements 2 Historically, the motivation that inspired Georg Cantor to develop set theory and point-set topology came from the following question:…”

Section: Literature Review -A History Of the Continuum Problemmentioning

confidence: 99%

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The Critics and Contributions of Mathematical Philosophy in Hong Kong Secondary Education

Shun¹

2020

AJAMS

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There are various schools of mathematical philosophy. However, none of them can be founded on mathematics alone. At the same time, there are two types of mathematical proof styles: Dialectic and algorithm mathematical proof. The relationship between proof and philosophy is to study philosophical problems with mathematical models. This type of proof is important to Hong Kong Secondary education. In addition, teachers should explain the connection between mathematics-based subjects, such as physics, so that lessons are more interesting rather than technical. Mathematics relates to nearly all other subjects, and as such has the role of a ‘public servant’ when it comes to serving them. One role of mathematics is to act as a ‘rational’ instrument for various subjects. This can be shown in many ancient human activities, such as Daoism and Liu Hiu, together with their symbolic representations. These examples are similar to Jewish culture; when discussing confidence, Abraham is often mentioned due to being the “Father of Confidence”. Thus, it may be said that mathematics is more than just a servant—it is also a cultural subject that has been recorded throughout history. To conclude, other than mathematical proof, Hong Kong teachers should also allow students to learn the cultural context behind various topics and subjects.

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Section: Literature Review -A History Of the Continuum Problemmentioning

confidence: 99%

“…The reply is that we can address problems such as transfinite induction and recursion etc. 2 These issues are related to hyper-computation 3 or super-Turing. This type of computing refers to models of computation, which give non-Turing-computable outputs.…”

Section: Cover Lettermentioning

confidence: 99%

The Critics and Contributions of Mathematical Philosophy in Hong Kong Secondary Education

Shun¹

2020

AJAMS

View full text Add to dashboard Cite

show abstract

An Investigation to Continuum Hypothesis

Cited by 1 publication

References 79 publications

The Critics and Contributions of Mathematical Philosophy in Hong Kong Secondary Education

The Critics and Contributions of Mathematical Philosophy in Hong Kong Secondary Education

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