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    In standard mathematical practice, biconditionals establi... — Carmelics
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    Challenges→The converse inclusion PSPACE ⊆ NPSPACE, while intuitive, is a definitional observation that must be stated explicitly to complete the biconditional equality claim.

    In standard mathematical practice, biconditionals established via proof don't require redundant restatement of 'obvious' directions; doing so suggests pedagogical rather than logical necessity.

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    Key Terms

    Biconditional(in formal logic)
    A logical statement that says two things are true if and only if each other is true; it's a two-way relationship (like saying 'you can vote if and only if you're 18').
    Pedagogical(describing the purpose Plato's scenarios served)
    Related to teaching and learning; designed to help students understand something.
    logical necessity(Distinguishing types of necessity)
    A property of statements that are true in all possible logical contexts, such as tautologies
    proof(Frege's formal system; the definition still used by logicians today)
    Any finite sequence of statements such that each statement is either an axiom of the formal system or follows from previous members of the sequence by a valid rule of inference.
    redundant

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    Start fresh with something unrelated.
    (contrasting with what the formula should actually be)
    Unnecessary or repetitive—extra without serving a purpose, like having two copies of the same tool.

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    The converse inclusion PSPACE ⊆ NPSPACE, while intuitive, is a definitional obse...

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    The converse inclusion PSPACE ⊆ NPSPACE, while intuitive, is a definitional obse...

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