Direct Proofs: attempt to prove statement is itself true Indirect Proofs: prove the negation of the statement is false. (proofs by contradiction: AFSOC - assume for the sake of contradiction)
Universal Statement: (\forall x \in S)P(x)
Direct Proofs: Let x\in S be arbitrary and fixed. Show P(x) holds.
Claim: (\forall x,y \in \mathbb{R})(4x^6+2y^2 \geq 4x^3 y)
Proofs: in English
Set Containment Proofs: show A \subset B by showing (\forall a \in A)(a\in B)
Double Containment Proof:
(see example 6.3 on lecture note Here)
QED
(\blacksquare): quod erat demonstrandum (proof is done)
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