B Converting Word-Problems into Equations and Vice Versa

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Every equation can be expressed in words, making it possible to convert any equation into a word problem. However, the ability to convert every word problem into an equation is less clear and depends on the definition of a word problem. Without precise definitions, the discussion remains philosophical and ambiguous. A deeper exploration into logic or formal language theory may provide clarity on this topic. Overall, the conversion between word problems and equations is feasible but requires careful consideration of definitions.
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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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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