Talk:Internal Direct Product Theorem
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Why do we have both https://proofwiki.org/wiki/Internal_Direct_Product_Theorem and https://proofwiki.org/wiki/Definition:Internal_Group_Direct_Product ? Why can't we just have a 3rd definition? BCLC (talk) 01:11, 28 October 2021 (UTC)
- The short answer is because it is introduced in the published works that we have available as an iff proof and not as an equivalent definition.
- We try to ensure that we introduce such equivalences as formal definitions only when it is documented as such in the literature.
- The thinking is that while an equivalence may be straightforward to formulate, its subsequent use as a definition may be dubious.
- Hence, if an author does consider such an equivalence useful as a definition, then we will follow that lead and include such in our database as a definition.
- Otherwise we may find ourselves overburdened with a large number of definitions, which becomes unwieldy to maintain.
- There are already cases where there are large number of definitions (in this context "large" means "over four") -- examples being: Definition:Normal Subgroup, Definition:Prime Number, Definition:Injection.
- No need to add greater complexity where it is unwarranted. --prime mover (talk) 19:44, 22 March 2022 (UTC)