Converting Word-Problems into Equations and Vice Versa

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SUMMARY

Every equation can be articulated as a word problem, as it can be expressed in verbal form. However, the reverse—converting every word problem into an equation—is less straightforward and depends on the precise definition of a word problem. The discussion emphasizes the need for clear definitions and logical frameworks, suggesting that without a solid understanding of formal logic or linguistic theory, the conversion process remains ambiguous. Participants are encouraged to explore these concepts further in specialized forums.

PREREQUISITES
  • Understanding of formal logic principles
  • Familiarity with linguistic theories, particularly Chomsky's hierarchy
  • Basic knowledge of mathematical equations and their verbal representations
  • Concepts of set theory relevant to logical statements
NEXT STEPS
  • Research formal logic and its applications in problem-solving
  • Study Chomsky's hierarchy of languages and its implications for word problems
  • Explore set theory concepts that relate to logical statements
  • Investigate methods for translating mathematical equations into natural language
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Mathematicians, educators, linguists, and anyone interested in the intersection of language and mathematics, particularly in problem-solving contexts.

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TL;DR
Convert word-problem into equation, and equation into word-problem..
Hi.
Can every word-problem be converted into equation?
Can every equation be converted into word-problem?

Thanks!
 
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pairofstrings said:
Summary:: Convert word-problem into equation, and equation into word-problem..

Hi.
Can every word-problem be converted into equation?
Can every equation be converted into word-problem?

Thanks!
What are your thoughts? Can you think of any counterexamples?
 
pairofstrings said:
Summary:: Convert word-problem into equation, and equation into word-problem..

Hi.
Can every word-problem be converted into equation?
Can every equation be converted into word-problem?

Thanks!
Hard to tell if neither is defined. As a rule of thumb: yes. Every equation can be spoken out, and thus described with words. On the other hand, the first question is less obvious, mainly because of a lack of meaning for word-problem. Let's assume that a problem ends with a question mark. Then it ends with whether a statement is true, hence an equation.

But unless you dive into real logic or the theory of formal languages, and define precisely what you mean, the question is meaningless, and philosophical at best. So please open another thread in the set theory and logic forum with a valid reference and precise definitions: either logical (which logic?), or linguistic, i.e. with Chomsky in mind.
 

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