What is Set Theory and How is it Used in Science?

Thread starter <<<GUILLE>>>
Start date Apr 27, 2005
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Set theory is a fundamental branch of mathematical logic that deals with the concept of sets, which are collections of objects. It provides the foundational framework for various mathematical disciplines and is essential in defining functions, relations, and cardinality. Set theory is widely used in science, particularly in fields like computer science, statistics, and probability, to model and analyze data. Key branches of set theory include naive set theory, axiomatic set theory, and descriptive set theory. Understanding set theory is crucial for grasping more complex mathematical concepts and their applications in scientific research.

Apr 27, 2005

<<<GUILLE>>>

Can someone introduce me to what the basics of set theory are, mean, are use in, have been created by, and it's branches?

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Apr 27, 2005

honestrosewater

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Check out http://plato.stanford.edu/entries/set-theory/ (SEOP is an excellent resource you may want to bookmark) and you can ask any questions you still have here.

Apr 28, 2005

<<<GUILLE>>>

thanks. I have as much as I needed.

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

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