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For example, when one is talking about a chemistry equation and they use values one wouldn't see in real life to illustrate a point better, or give a specific example that requires extra steps that likely won't be required in the usual cases, what would they include to say this is an example that wouldn't(or less likely to) exist in real life, but it is picked as it illustrates the point better ?

A general idiom/phrase for unarbitrary as in the example was picked with care, it isn't arbitrary would work as well.

Thanks in advance.

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This is often called a “contrived example”. Cambridge gives the definition of contrived as “too obviously designed to produce a particular result, and therefore not seeming to happen naturally”, and provides an example that suggests that the word has negative connotations, but in scientific and technical writing, the negative connotations simply do not exist.

  • Seconding contrived depending on the context. Contrived is less about inventing some imaginary or fanciful example that happens to fit perfectly and more, to my ears, about attempting to force an example that's slightly off to prove a point. – Turkeyphant May 29 at 22:27
  • Thanks! I am not entirely satisfied due to the negative connotation, though there doesn't seem to be any better alternative. english.stackexchange.com/questions/409157/… – Lacey May 29 at 23:43
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A "toy problem" may the word you're looking for.

Specifically, this refers to problems and examples in scientific fields that are not of practical interest, but of pedagogical use and interesting to consider theoretically.

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I would call it a theoretical example (or model).

[Merriam-Webster]

1 : existing only in theory : HYPOTHETICAL
// gave as an example a theoretical situation
2 a : relating to or having the character of theory : ABSTRACT
2 b : confined to theory or speculation often in contrast to practical applications : SPECULATIVE
// theoretical physics

While examples that are theoretical can exist in reality, they often either don't, or at least don't in exactly the same way. Theoretical models are used as methods of explanation (and to discuss idealized reality) rather than to present actual 1-1 correspondence.

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