# Equations and Word-problems

pairofstrings
TL;DR 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!

Mentor
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?

Mentor
2022 Award
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.