Prerequisite Before Learning Set Theory

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    Set Set theory Theory
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Discussion Overview

The discussion revolves around the prerequisites for learning set theory, including the necessary mathematical background and skills. Participants explore the foundational knowledge required before delving into set theory, with references to various mathematical subjects and the concept of "mathematical maturity." The conversation also touches on the relationship between set theory and other advanced topics like general topology.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that there are no strict prerequisites for set theory, but a certain level of "mathematical maturity" is necessary to understand the definitions and theorems.
  • One participant expresses a desire for a general overview of set theory and questions whether it is foundational compared to other mathematical theories.
  • Another participant mentions that a course focused on writing proofs might be beneficial before studying set theory, though this may depend on the specific course structure.
  • There is a discussion about the nature of mathematical proofs, with some participants arguing that informal proofs are acceptable while others emphasize the importance of correctness in proofs.
  • Elementary set theory has been taught at basic educational levels, but a more formal treatment may require knowledge of symbolic logic or proof theory.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of prerequisites for set theory, with some asserting that a foundational understanding is essential while others argue that it is accessible without prior knowledge. The discussion remains unresolved regarding the best approach to prepare for studying set theory.

Contextual Notes

Participants mention the importance of understanding proof theory and mathematical reasoning, but there is no consensus on specific courses or subjects that should be prioritized before studying set theory.

anonymous007
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I am in calculus, I was just wondering what math classes (or prerequisites) before trying to learn set theory. For example Should I learn multivariable calculus, linear algebra, etc. (or what)?
 
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I'm finishing up Calc I in my senior year in HS and I've been reading Set Theory, you just need a dedicated mind to understand some of this new stuff lol.
 
anonymous007 said:
I am in calculus, I was just wondering what math classes (or prerequisites) before trying to learn set theory. For example Should I learn multivariable calculus, linear algebra, etc. (or what)?

There aren't any real prerequisites because it's a fundamental subject, but some "mathematical maturity" is needed to appreciate the relevance of some of the definitions and theorems. Which aspects of the subject are of interest you?
 
I would just like to get a general overview of the whole subject. I was reading stuff off of the internet and it said that set theory was the basis for many mathematical concepts (am I right or is there more basic theories to study before this?) I would like to get more involved in the math world so I thought that this would be a start. I just don't know where to start in order to get ready for this subject and what I need to study up on before attempting to read material on set theory.

actually (in the long run) I would like to eventually study general topology, so I guess my real question is what mathematical subjects and theories would I need to study before this (is set theory a subject I should learn first, and if so what do I need to study to be able to study set topology)?
 
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Depending on the set theory course, you may need first a course where you learn to write proofs. Or, that may be the emphasis of the set theory course itself. Depends on the course.
 
bpet said:
but some "mathematical maturity" is needed

Yes, this means you should have arrived at the stage where you no longer bother about if your proofs are correct, because you adopted the mathematicians' attitude to write informal proofs and hope, believe that everything will be fine. With this you are well prepared for standard set theory courses and advanced studies in mathematics.
 
mathaino said:
Yes, this means you should have arrived at the stage where you no longer bother about if your proofs are correct, because you adopted the mathematicians' attitude to write informal proofs and hope, believe that everything will be fine. With this you are well prepared for standard set theory courses and advanced studies in mathematics.

Mathematicians certainly are not just writing informal proofs and hoping that everything will be fine, and they certainly DO bother to check whether the proofs are correct.
 
Elementary set theory has been taught to grammar school kids; they called this the "new math" back in the '60s. Now, if you want a formal and more complex treatment of it, where proofs are involved, it doesn't hurt to have a symbolic logic course. Barring that, as g_edgar states, any course where learning proof theory is involved would help - even geometry, but knowing "how" deduction works is critical to all this.
 

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