Category:Proofs by Contradiction
Jump to navigation
Jump to search
(previous page) (next page)
Pages in category "Proofs by Contradiction"
The following 200 pages are in this category, out of 666 total.
(previous page) (next page)1
A
- Abelian Group Factored by Prime
- Absolute Value is Many-to-One
- Absolute Value of Components of Complex Number no greater than Root 2 of Modulus
- Absolutely Convergent Product Does not Diverge to Zero
- Absolutely Convergent Product Does not Diverge to Zero/Proof 1
- Absolutely Convergent Product Does not Diverge to Zero/Proof 2
- Accumulation Points of Sequence of Distinct Terms in Infinite Particular Point Space
- Additive Group and Multiplicative Group of Field are not Isomorphic
- Template:AimForCont
- Alexander's Compactness Theorem
- Alexandroff Extension of Rational Number Space is Connected
- Algebraic Element of Degree 3 is not Element of Field Extension of Degree Power of 2
- Algebraic Element of Field Extension is Root of Unique Monic Polynomial of Minimal Degree
- Altitude, Median and Perpendicular Bisector Coincide iff Triangle is Isosceles
- Annihilating Polynomial of Minimal Degree is Irreducible
- Anomalous Cancellation on 2-Digit Numbers
- Antiassociative Operation has no Idempotent Elements
- Antiperiodic Element is Multiple of Antiperiod
- Archimedean Principle/Variant
- Area of Circle
- Area of Circle/Proof 3
- Arens-Fort Space is not Countably Compact
- Arens-Fort Space is not First-Countable
- Asymmetric Relation is Antireflexive
- Axiom of Choice Implies Zorn's Lemma
- Axiom of Choice Implies Zorn's Lemma/Proof 2
- Axiom of Pairing from Powers and Replacement
B
- Backwards Induction
- Basic Universe has Infinite Number of Elements
- Basic Universe is not Set
- Beatty's Theorem
- Beatty's Theorem/Proof 1
- Beatty's Theorem/Proof 2
- Bernstein's Theorem on Unique Global Solution to y''=F(x,y,y')
- Between two Rational Numbers exists Irrational Number/Lemma 1
- Between two Rational Numbers exists Irrational Number/Lemma 2
- Bolzano-Weierstrass Theorem/General Form
- Boolean Prime Ideal Theorem/Extension Lemma
- Bounded Above Subset of Real Numbers/Examples/Open Interval from 0 to 1
- Bounded Below Subset of Real Numbers/Examples/Open Interval from 0 to 1
- Bounded Below Subset of Real Numbers/Examples/Real Numbers
- Brouwer's Fixed Point Theorem/One-Dimensional Version
- Brouwer's Fixed Point Theorem/One-Dimensional Version/Proof Using Connectedness
- Bézout's Lemma/Euclidean Domain
C
- Cantor's Theorem
- Cantor's Theorem (Strong Version)
- Cantor's Theorem (Strong Version)/Proof 2
- Cantor's Theorem/Proof 1
- Cardinality of Mapping
- Cauchy's Inequality
- Cauchy's Inequality/Proof 1
- Center of Group of Order Prime Cubed
- Characterisation of Jacobson Radical
- Characterisation of Non-Archimedean Division Ring Norms/Corollary 2
- Characteristic of Field by Annihilator/Characteristic Zero
- Characteristic of Field by Annihilator/Prime Characteristic
- Characterization of Closure by Open Sets
- Characterizing Property of Infimum of Subset of Real Numbers
- Characterizing Property of Supremum of Subset of Real Numbers
- Chords do not Bisect Each Other
- Circle is Bisected by Diameter
- Circle is Bisected by Diameter/Proof 1
- Class has Subclass which is not Element
- Clopen Set contains Components of All its Points
- Closed Balls Centered on P-adic Number is Countable/Lemma
- Closed Extension Topology is not Hausdorff
- Closed Set of Uncountable Finite Complement Topology is not G-Delta
- Closed Set/Complex Analysis/Examples/Closed Unit Circle
- Closed Topologist's Sine Curve is not Path-Connected
- Closed Unit Interval is not Countably Infinite Union of Disjoint Closed Sets
- Closure of Pointwise Operation on Algebraic Structure
- Compact First-Countable Space is Sequentially Compact
- Compact Hausdorff Topology is Maximally Compact
- Compact Hausdorff Topology is Minimal Hausdorff
- Compact Set of Rational Numbers is Nowhere Dense
- Compact Sets in Countable Complement Space
- Compact Subspace of Linearly Ordered Space/Lemma
- Compact Subspace of Metric Space is Sequentially Compact in Itself
- Comparison Test for Convergence of Power Series
- Complement of Prime Ideal of Ring is Multiplicatively Closed
- Complement of Symmetric Relation
- Complex Numbers cannot be Extended to Algebra in Three Dimensions with Real Scalars
- Complex Numbers cannot be Ordered Compatibly with Ring Structure
- Complex Numbers cannot be Ordered Compatibly with Ring Structure/Proof 1
- Complex Numbers cannot be Ordered Compatibly with Ring Structure/Proof 2
- Complex Numbers cannot be Ordered Compatibly with Ring Structure/Proof 3
- Complex Numbers under Multiplication do not form Group
- Complex Sine Function is Unbounded
- Component of Finite Union in Ultrafilter
- Composition of 3 Mappings where Pairs of Mappings are Bijections
- Condition for Composite Relation with Inverse to be Identity
- Condition for Denesting of Square Root/Lemma
- Condition for Differentiable Functional to have Extremum
- Condition for Open Extension Space to be Separable
- Condition for Relation to be Transitive and Antitransitive
- Condition for Repunits to be Coprime
- Condition for Uniqueness of Increasing Mappings between Tosets
- Conditions for Floor of Log base b of x to equal Floor of Log base b of Floor of x
- Conditions for Floor of Log base b of x to equal Floor of Log base b of Floor of x/Proof 1
- Congruence Modulo Integer/Examples/531 not equiv 1236 mod 7561
- Connected Subspace of Linearly Ordered Space
- Continuous Function on Compact Space is Bounded
- Continuous implies Increasing in Scott Topological Lattices
- Convergent Real Sequence has Unique Limit
- Convergent Real Sequence has Unique Limit/Proof 1
- Convergent Sequence in Normed Vector Space has Unique Limit
- Converse Hinge Theorem
- Coset/Examples/Subgroup of Infinite Cyclic Group
- Countable Complement Space is not Countably Compact
- Countable Complement Space is not First-Countable
- Countable Finite Complement Space is not Locally Path-Connected
- Countable Finite Complement Space is not Path-Connected
- Countably Infinite Set in Countably Compact Space has Omega-Accumulation Point
- Cover of Interval By Closed Intervals is not Pairwise Disjoint
- Crossbar Theorem
- Cycle does not Contain Subcycles
D
- Decomposition into Product of Power of 2 and Odd Integer is Unique
- Dedekind's Theorem
- Dedekind's Theorem/Proof 2
- Dedekind's Theorem/Proof 3
- Degree of Vertex/Examples/Impossible Order 4 Graph
- Dense-in-itself Subset of T1 Space is Infinite
- Derivative of Exponential Function/Proof 5/Lemma
- Deterministic Time Hierarchy Theorem
- Diameter of Closure of Subset is Diameter of Subset
- Difference of Consecutive terms of Coherent Sequence
- Differential of Differentiable Functional is Unique/Lemma
- Dihedral Group D4 is not Internal Group Product
- Dihedral Group D4 is not Internal Group Product/Proof 1
- Discrete Space is Compact iff Finite
- Discrete Subgroup of Hausdorff Group is Closed
- Disjoint Permutations Commute
- Distance from Subset of Real Numbers to Supremum
- Distance from Subset of Real Numbers to Supremum/Proof 1
- Divergent Sequence may be Bounded
- Divergent Sequence may be Bounded/Proof 1
- Division Theorem for Polynomial Forms over Field
- Division Theorem for Polynomial Forms over Field/Proof 1
- Division Theorem/Positive Divisor/Positive Dividend/Existence
- Division Theorem/Positive Divisor/Positive Dividend/Existence/Proof 1
- Division Theorem/Positive Divisor/Positive Dividend/Uniqueness
- Division Theorem/Positive Divisor/Positive Dividend/Uniqueness/Proof 1
- Division Theorem/Positive Divisor/Uniqueness
- Division Theorem/Positive Divisor/Uniqueness/Proof 1
- Divisor of One of Coprime Numbers is Coprime to Other
- Divisor of One of Coprime Numbers is Coprime to Other/Proof 1
- Divisors of Power of Prime
- Double Pointed Topology is not T0
- Double Pointed Topology is not T0/Proof 2
E
- Edgeless Graph of Order n has n Components
- Element Depends on Independent Set iff Union with Singleton is Dependent/Lemma
- Element of Matroid Base and Circuit has a Substitute/Lemma 2
- Element of Principal Ideal Domain is Finite Product of Irreducible Elements
- Elementary Row Operation on Augmented Matrix leads to Equivalent System of Simultaneous Linear Equations/Corollary 2
- Empty Set as Subset
- Empty Set from Principle of Non-Contradiction
- Equal Alternate Angles implies Parallel Lines
- Equality of Ordered Pairs/Necessary Condition
- Equality of Ordered Pairs/Necessary Condition/Proof from Empty Set Formalization
- Equality of Ordered Pairs/Necessary Condition/Proof from Wiener Formalization
- Equivalence of Definitions of Antisymmetric Relation
- Equivalence of Definitions of Arborescence
- Equivalence of Definitions of Ceiling Function
- Equivalence of Definitions of Closed Set in Normed Vector Space
- Equivalence of Definitions of Compact Topological Space
- Equivalence of Definitions of Connected Topological Space
- Equivalence of Definitions of Connected Topological Space/No Union of Separated Sets implies No Continuous Surjection to Discrete Two-Point Space
- Equivalence of Definitions of Countably Compact Space
- Equivalence of Definitions of Floor Function
- Equivalence of Definitions of Infimum of Real-Valued Function
- Equivalence of Definitions of Infinite Cyclic Group
- Equivalence of Definitions of Infinite Order Element
- Equivalence of Definitions of Injection
- Equivalence of Definitions of Injection/Definition 1 iff Definition 1 a
- Equivalence of Definitions of Injection/Definition 1 iff Definition 4
- Equivalence of Definitions of Irreducible Space
- Equivalence of Definitions of Irreducible Space/3 iff 7
- Equivalence of Definitions of Isolated Point
- Equivalence of Definitions of Matroid
- Equivalence of Definitions of Matroid/Definition 1 implies Definition 4
- Equivalence of Definitions of Minimal Element
- Equivalence of Definitions of Non-Unity Variant of Echelon Form
- Equivalence of Definitions of Order of Group Element
- Equivalence of Definitions of Prime Ideal of Commutative and Unitary Ring
- Equivalence of Definitions of Prime Number
- Equivalence of Definitions of Real Inverse Hyperbolic Cosine
- Equivalence of Definitions of Supremum of Real-Valued Function
- Equivalence of Definitions of T2 Space
- Equivalence of Definitions of Totally Separated Space
- Equivalence of Definitions of Transitive Relation
- Equivalence of Definitions of Ultraconnected Space
- Equivalence of Definitions of Ultraconnected Space/1 iff 3
- Equivalence of Definitions of Ultrafilter on Set
- Equivalence of Definitions of Ultrafilter on Set/Definition 1 iff Definition 3
- Equivalence of Definitions of Ultrafilter on Set/Equivalence of Definitions 1, 2 and 3
- Equivalence of Formulations of Axiom of Infinity for Zermelo Universe
- Equivalence of Well-Ordering Principle and Induction
- Equivalence of Well-Ordering Principle and Induction/Proof/PCI implies WOP
