RA:567
Negate, then prove
Proof FoundationsReal Analysis I · Proof technique
8 min◆◇◇◇◇
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Problem results
50 shown of 569 exact matches · 569 in the catalog
RA:568
A direct inclusion proof
Proof FoundationsReal Analysis I · Proof technique
8 min◆◇◇◇◇
Outcome unavailableProof FoundationsReal Analysis I · Concept & counterexample
10 min◆◇◇◇◇
Outcome unavailableRA:001
Irrationality beyond sqrt(2)
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:002
Rationals acting on irrationals
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:003
Quantifier negation drill
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
11 min◆◇◇◇◇
Outcome unavailableRA:004
Finite versus infinite De Morgan
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:005
Images and preimages
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
15 min◆◆◇◇◇
Outcome unavailableRA:006
One-to-one and onto models
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
15 min◆◆◇◇◇
Outcome unavailableRA:007
Triangle inequality variants on R
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:008
Induction on a recursive sequence
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
11 min◆◇◇◇◇
Outcome unavailableRA:009
Nested sets can mislead
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
15 min◆◆◇◇◇
Outcome unavailableRA:010
Epsilon comparison trap
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
15 min◆◆◇◇◇
Outcome unavailableRA:011
Infimum definition and epsilon test
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:012
Maximum versus supremum
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
11 min◆◇◇◇◇
Outcome unavailableRA:013
Supremum under translation
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:014
Supremum under scaling
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:015
Supremum of a sumset
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:016
Infimum through negation
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
11 min◆◇◇◇◇
Outcome unavailableRA:017
Monotonicity of supremum
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
15 min◆◆◇◇◇
Outcome unavailableRA:018
Separating sets by a number
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
15 min◆◆◇◇◇
Outcome unavailableRA:019
Cut property and completeness
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
19 min◆◆◆◇◇
Outcome unavailableRA:020
Nested interval property
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
15 min◆◆◇◇◇
Outcome unavailableRA:021
Existence of sqrt(2)
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
15 min◆◆◇◇◇
Outcome unavailableRA:022
General nth roots
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
15 min◆◆◇◇◇
Outcome unavailableRA:023
Finite versus infinite union suprema
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
15 min◆◆◇◇◇
Outcome unavailableRA:024
Near-supremum elements
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:025
Archimedean property
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:026
No infinitesimals in R
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:027
Density of Q
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
19 min◆◆◆◇◇
Outcome unavailableRA:028
Density of irrational numbers
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:029
Supremum of rational traces
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:030
Dyadic rationals are dense
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
19 min◆◆◆◇◇
Outcome unavailableRA:031
Decimals as supremum approximations
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:032
Epsilon order criterion
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:033
Rational gap in Q
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:034
Interval intersection diagnostics
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Concept & counterexample
19 min◆◆◆◇◇
Outcome unavailableRA:035
Exponent laws from suprema
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
19 min◆◆◆◇◇
Outcome unavailableRA:036
Cancellation from field axioms
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:037
Zero products
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:038
Positive squares
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:039
Complex numbers cannot be ordered as a field
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:040
Lexicographic order on C
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:041
Extended reals are not a field
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:100
Dedekind cut addition
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
19 min◆◆◆◇◇
Outcome unavailableRA:043
Why cuts need no largest element
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
19 min◆◆◆◇◇
Outcome unavailableRA:044
Conjugation identities
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
15 min◆◆◇◇◇
Outcome unavailableRA:045
Product formula for modulus
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
19 min◆◆◆◇◇
Outcome unavailableRA:046
Complex triangle inequality
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Calculation / construction
15 min◆◆◇◇◇
Outcome unavailableRA:047
Reverse triangle inequality
Catalog record · grading packet pending reviewFoundations & CompletenessReal Analysis I · Proof technique
19 min◆◆◆◇◇
Outcome unavailable