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▾
Bridge course
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Countable and uncountable sets
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Proof techniques
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Example of a nonconstructive proof
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Direct proof
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Disproof by counterexample
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Proof by cases
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Proving properties of absolute value
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Proof by contrapositive
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Proof by contradiction
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Proof by induction
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Proof by strong induction
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Proving de Moivre's theorem
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Visual proof
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Challenge
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Relations
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Equivalence relations
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Intersection of equivalence relations
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Representing relations using matrices
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Combining relations
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Composition of relations
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Inverse of composite relation
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Representing relations using digraphs
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Properties of relations
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Proving equivalence relations
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What is a relation?
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Finding the inverse of a relation on a finite set
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Functions (bridge course)
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Injective, surjective, and bijective
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Intro
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Is it bijective? (infinite domain)
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Is it injective?
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Is it surjective?
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Proof: Composite of surjections is surjection
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Proving properties of injective, surjective, and bijective functions
›
Bridge course
›
Proof techniques
Example of a nonconstructive proof
There exist irrational numbers \(a\) and \(b\) such that \(a^b\) is rational.
924
A fascinating non-constructive proof
discovermaths
71656
Irrational to Irrational Power is Rational! Incredible Proof
Math at Andrews
51148
irrational^irrational=rational?
blackpenredpen
72386
There Exists Two Irrational Numbers a and b s.t. a^b is Rational
Math For Life