Problem library

Find a problem

Search by course or topic.

Search problems

Clear

Filters · 2 active

Area

AllMathPhysics

SubjectCourseTopic

Topic choices for Real Analysis I are shortened. Search still covers every problem.

StatusSkillProblem styleFind a private labelPrivate labelFavorites

Some filter menus are shortened. Search still checks every problem.

Browsing still works.Sign in to use progress, saved problems and private labels. Problem search and previews remain available.

Progress labels

IndependentSolved with helpIncorrect / unresolvedDraft in progressNot attemptedReview due

Problem results

ProblemsClear skill: Proof Foundations Build a practice set

RA:001Negating alternating quantifiers

Proof FoundationsQuantifier NegationArchimedean LanguageLogical Equivalence

Proof language, sets, functions, and quantifiersReal Analysis I · Concept & counterexample

RA:002Contrapositive versus converse

Proof FoundationsContrapositiveTruth ValuesImplication

Proof language, sets, functions, and quantifiersReal Analysis I · Concept & counterexample

RA:003Rational plus irrational

Proof FoundationsRational ClosureIrrational NumbersAdditive Inverses

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:004Even square forces even integer

Proof FoundationsParityDivisibilityContrapositive

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:005Irrationality of square root two

Proof FoundationsSqrt TwoLowest TermsParity Descent

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:006De Morgan by element chasing

Proof FoundationsSet ExtensionalityDE Morgan LawComplements

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:007Power-set inclusion

Proof FoundationsPower SetSubset RelationSingleton Witness

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:008Preimage of indexed intersections

Proof FoundationsPreimageIndexed IntersectionFunction Membership

Proof language, sets, functions, and quantifiersReal Analysis I · Calculation

RA:009Image of an intersection

Proof FoundationsSet ImageInjective FunctionsIntersection Counterexample

Proof language, sets, functions, and quantifiersReal Analysis I · Calculation

RA:010Injective compositions

Proof FoundationsFunction CompositionInjectivityRange Restriction

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:011Surjective compositions

Proof FoundationsSurjective FunctionsComposition RangeFinite Counterexample

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:012Congruence modulo five

Proof FoundationsEquivalence RelationModular CongruenceInteger Divisibility

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:013Equality of equivalence classes

Proof FoundationsEquivalence ClassesSet ExtensionalityTransitive Relations

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:014Sum of the first odd integers

Proof FoundationsMathematical InductionFinite SumsOdd Numbers

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:015Exponential versus linear growth

Proof FoundationsInduction InequalityExponential GrowthEquality Cases

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:016Existence of a prime divisor

Proof FoundationsStrong InductionPrime DivisorsFactorization

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:017A recursive affine sequence

Proof FoundationsRecursive SequenceClosed FormInduction

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:018Finite geometric sum

Proof FoundationsGeometric SeriesFinite SumInduction Algebra

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:019Enumerating the integers

Proof FoundationsCountable SetsInteger EnumerationSurjective Map

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:020Diagonal enumeration of pairs

Proof FoundationsCartesian ProductDiagonal EnumerationCountability

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:021Countable union theorem

Proof FoundationsCountable UnionEnumerationsPairing Function

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:022Countability of the rationals

Proof FoundationsRational NumbersQuotient RepresentationCountable Image

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:023Cantor diagonal binary sequence

Proof FoundationsCantor DiagonalBinary SequencesUncountability

Proof language, sets, functions, and quantifiersReal Analysis I · Proof

RA:024Negation of sequence convergence

Proof FoundationsSequence ConvergenceEpsilon NegationQuantifier Order

Proof language, sets, functions, and quantifiersReal Analysis I · Concept & counterexample

Showing 24 of 33 matching problems.

Problem library

Find a problem

Search by course or topic.