Proposition
Summary
A proposition is a statement that is either true or false. In classical logic, each proposition has exactly one of the two truth values, true or false. For example, "" is a true proposition, and " is even" is a false proposition. A question or a command is not a proposition, because it has no truth value.
Remarks
Letters such as , and usually denote propositions. An open sentence such as "" is not a proposition until has a value. It is a predicate. The connectives negation, conjunction and disjunction make new propositions from given propositions.
Explanations
L1 human
A proposition is a sentence that you can mark with "true" or "false". "It rains in Paris now" is a proposition, because it is true or false at a given time. "Close the door" is not a proposition, because it is neither true nor false.
What this node needs for W2
- edge defines in: at least one definition (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
The writing levels say how complete the text of a node is. They do not measure its truth.
What depends on this
467 nodes use this node, directly or through other nodes.
- Closure is the set of limits of sequences 003QP7A8HG
- Variance 007QED3E0Y
- Finite intersection property 00BWV5CKCF
- Hasse diagram 00EYM7MDKS
- Prior probability 00NBBSXRQS
- Compact set 00R0X1WGPX
- Second-countable space 00RE1R4W7N
- Event 00SQGJNRTB
- Partial order 011C29Q1S1
- Chernoff bound 014PEBGDYF
- Chapman–Kolmogorov equation 01APZ8GDQH
- Bias of an estimator 01BD2TFFP4
- Totally disconnected space 01CYW8S04D
- Urysohn's lemma 01EY3VR7ZD
- Composition of injections is injective 01FPXMTBX1
- Order of cardinals 01GTP8M5RG
- Equivalence classes form a partition 01HT2CH8BH
- Triangle inequality for a metric 01M6CW9VM6
- Antisymmetric relation 01MGYYBB9R
- Infinite set 01MKW4R283
- Isolated point 01PKQYTTMT
- Composition of relations 01SWBKDAWA
- Bijective iff it has a two-sided inverse 01VG2A0BHW
- Cantor set is closed 01VT24J1SD
- Identically distributed random variables 01X8YSDTBW
- Constructive proof 01XM7JEKHY
- Open set 01ZQQDCERP
- Law of the unconscious statistician 01ZWX875AT
- Well-founded relation 0230ECX1Q5
- Left inverse 02486SD328
- Density of the normal distribution 027JF1FBB0
- Exponential distribution 028Z8WC5Y9
- Covariance matrix 02CBHV4ZZQ
- Open balls form a basis of the metric topology 02EEX96DFS
- Chebyshev's inequality 02HZ1BK3MW
- Isometries are injective 02J4G4J4TJ
- Characteristic function of a sum of independent random variables 02JGYG0T7M
- Stationary distribution 02KYGSCTCN
- Closure is closed 02TZDKG50Q
- Bernoulli process 02XPXR1FBK
- Total order 0316AYH1SC
- Markov chain 033TJBZDG0
- Statistic 036756NFD6
- Arzelà–Ascoli theorem 0381S8Z5P0
- Law of total variance 03BY5XTNA4
- Variance of the normal distribution 03EESZDB9A
- Equivalence of norms in finite dimension 03MC70ZRNR
- Torus 03NM7DZXXC
- Cauchy–Schwarz inequality for expectations 03PGHKAJG3
- Lebesgue number lemma 040CFNJEAP
- Continuous bijection from a compact space to a Hausdorff space is a homeomorphism 0430ETCMKD
- Product metric 044D4AQV8V
- Monotonicity of probability 0464Z0JP2E
- Möbius strip 04AJE0M271
- Correlation coefficient 04CTY6XYWN
- Variance under translation 04CYN5G6RY
- Almost sure convergence 04P7D63W8P
- Law of total expectation 04RRB6HM00
- Zorn's lemma 04RXTQA5ZA
- Product topology on an arbitrary product 04S9HX3GAP
- Contrapositive 04T1CT7212
- Sigma-algebra 04WSW8T3SY
- Probability density function 04YG690N5V
- The real numbers are uncountable 0518MM6BE1
- Compact iff complete and totally bounded 054Q5PW5GX
- Expectation of a product of independent random variables 05AW1G0WE1
- Closed ball 05DSV40EB9
- Likelihood function 05FSTXM92W
- Union of a family of sets 05GK32H72H
- T1 space 05GQJXBP3F
- Homeomorphism 05GZ11PWRY
- Composition of continuous maps is continuous 05NK26G0DR
- Markov's inequality 05PWWHYBX5
- Truth table 05RSK4Q657
- Standard score 05RZ4YZG4E
- Negation of an existential statement 05SZQKH75K
- Poisson point process 05TG0SE4HT
- Gamma distribution 06395GBNWD
- Metric space 063W5JMY85
- Inclusion of a subspace is continuous 065J822CKN
- De Moivre–Laplace theorem 065X9S8CM3
- Closed subsets of compact sets are compact 066HW6D9A7
- The integers are countable 066RJJVWH9
- Closure in a metric space 068P0P32DW
- Diameter of a set 0692CGQF00
- Heine–Cantor theorem 06B8BNJCD6
- Basis of a topology 06EX0FHBTF
- Logical equivalence 06GYGS41JK
- Convergence of a sequence in a metric space 06JYPJ4WHH
- Buffon's needle problem 06X5PF6YFP
- Kolmogorov's zero–one law 073Q8Z94KG
- Correspondence between equivalence relations and partitions 074482Q7CD
- The reals have the cardinality of the continuum 075PM9FH7A
- Independent random variables are uncorrelated 077GN9HDR6
- Convolution of probability distributions 07CHJ5YX28
- Lipschitz maps are uniformly continuous 07DCKDXRBP
- Composition of surjections is surjective 07EH4R3RVQ
- Function composition 07HF9YCWPP
- Union 07KVB4JSC7
- Continuity at a point of a topological space 07N7W5C29X
- Heine–Borel theorem 07PFYV65MB
- Normal distribution 07RXBVTVZB
- Distance from a point to a set 07TXYYVYZR
- Absolutely convergent series in a Banach space converge 082MGNWNA8
- Equivalence class 082RMRSY26
- Intersection of a family of sets 0839XNQXDK
- Mean of the Poisson distribution 086HEVXR9Z
- Predicate logic 086QKPF0A6
- Isometry 0878DN3WCS
- Statistical hypothesis test 087P03NEND
- Binary relation 08EJC6Q25H
- Equinumerous sets 08EJHHMB5R
- Complete metric space 08EWT7J0SC
- Product of countable sets is countable 08G4XH86JC
- Distributive laws for sets 08N6EVA7DV
- Sequence spaces lp 08P6T2WH6R
- Independence means the joint law is the product of the marginals 08QCA2F1NX
- Topological embedding 08SVRVHJNY
- Median 08W2CW8PKW
- Comparison of topologies 08XFJJ8EYW
- Geometric probability 0924BCD257
- Domain 093CM69AGS
- Riesz's lemma 097C7KCAT5
- Intermediate value theorem for connected spaces 098C0KZZAP
- Dirac measure 099SXAG014
- Necessary and sufficient conditions 09BJQQB3VS
- Partition of a set 09CCE86A6D
- Open sets characterised by neighbourhoods 09CJ00H3NW
- Closed sets contain their limits 09GQ3ZTQJ9
- Completeness of the space of bounded continuous functions 09GRCZVR5E
- Method of moments 09J1H07VAH
- Propositional logic 09K9MWD2QQ
- Metrizable space 09KDHB82SG
- Finite intersection of open sets is open 09NDE9V7X1
- De Morgan's laws 09PKJKA6J0
- Mean of the normal distribution 09PR1V6RWR
- Independent sigma-algebras 09T8ZHST1V
- Intersection of closed sets is closed 09YMV8H4X5
- Product of compact sets is compact 09ZKE5XQ74
- Open sets of a metric space 0A26X79RTB
- Metric topology 0A6YRNZB2R
- Baire category theorem 0A7KGAYHGV
- Schröder–Bernstein theorem 0A9V6RKQG6
- Finite-dimensional normed spaces are complete 0ABP2F2ZP7
- Metrizable spaces are normal 0AD0BZ49DW
- Normal space 0AJ646N339
- Independent and identically distributed random variables 0AJN7WHBJZ
- Classical definition of probability 0AKNPYQ04R
- Pairwise independent events that are not mutually independent 0AR4B3K5QD
- Marginal distribution 0AXP2Z5N9H
- Complement 0B1FSS1VZW
- Moment-generating function of the normal distribution 0B1G4E21G7
- Open balls are open 0B2305GNAZ
- Quantile function 0B3Q3XDM5X
- Universal quantifier 0B88PQTJ66
- Continuity via closed sets 0B8GPXFSP7
- Mathematical proof 0B94TKFQJX
- Connected subsets of the real line are intervals 0B9ZQFMQNV
- Proof by contrapositive 0BB5TPGQ1N
- Finite set 0BBTH3YSZA
- Power set 0BC7KX51Z8
- Banach space 0BDTTM24DP
- Weak law of large numbers 0BFDHF2H7N
- Universal set 0BPYRMHJ48
- Multiplication rule 0BS3RMX8HM
- Borel sigma-algebra 0BVHZXWKCD
- Addition rule for two events 0BZQ6ZX584
- Random walk 0C08YMV95H
- Linear maps on finite-dimensional spaces are continuous 0C13E623WD
- Random variable with a density 0C21RZG5V2
- Interior 0C38S0KMJK
- Uncorrelated random variables that are not independent 0C6J8BQXVR
- Sequential compactness 0CARW59WD2
- Kurtosis 0CBQVVNBMP
- Martingale 0CDVK9RQBH
- Subbasis 0CHR35YNJQ
- Topological space 0CNQXVBHCX
- Box topology 0CTM1EHG9P
- Transitive relation 0CYRECG2YQ
- Dense set 0D198GPMTJ
- Tautology 0D1AHYPM8N
- Restriction of a function 0D2MXBV21T
- A set is closed iff it equals its closure 0D2W7FS52T
- Baire space 0D5KR33H7X
- Subspace topology 0D5YHQGDJY
- Variance of a sum 0D86GJEZ39
- Limits are unique in Hausdorff spaces 0D8T984XEE
- Connected space 0D939CMME7
- Probability axioms 0DAX8PMAJ4
- Mean of the geometric distribution 0DB0R4N5XX
- Open ball 0DC3MPR7C9
- Expected value 0DCT0QZVQ1
- Right inverse 0DDPZAG5ER
- Strong law of large numbers 0DFWHQ839T
- Covariance 0DJ8W3HP2D
- Random variable 0DKRR22AEQ
- Closure 0DRKT1QJR7
- The rationals are countable 0DS9KWFDK2
- Set difference 0DT0TCV75N
- Base rate fallacy 0E44JMG6NV
- Law of total probability 0E5G5FMT2R
- Independence of two random variables 0E9502NT92
- Range of a function 0E9GTAV478
- Counterexample 0ED72CTBNP
- Neyman–Pearson lemma 0EE19CFEEF
- Convergence in probability 0EFDDXTVD6
- Boole's inequality 0EGSEE9J9R
- P-value 0EHYZFZ4PK
- Epsilon-delta continuity in metric spaces 0EKGKY5TGH
- Chi-squared test 0EN0V3NY20
- Continuous image of a connected set is connected 0EPD87YVG8
- Convergence in probability implies convergence in distribution 0EPTDZPJ83
- Central limit theorem 0EPZC4Z1FC
- Locally compact space 0EQMWQ4WMJ
- 68–95–99.7 rule 0EYQ03XCR3
- Cantor's intersection theorem 0EZBG8SKJM
- Well-order 0F1D6PK9RZ
- Transition matrix 0F1KBVY161
- Conditional variance 0F1SN93KXE
- Bounded linear maps are continuous 0F3K4C7XYW
- Codomain 0F9JHP8AJN
- Closed subsets of complete spaces are complete 0FBXJZX3MK
- Subset 0FE8Q5S42Y
- Universal property of the quotient topology 0FF2FJ8CH2
- Preimage of a set 0FGCFY1AZX
- Epsilon-delta uniform continuity 0FHSDCQACY
- Conditional probability 0FJB06AD2P
- Lévy's continuity theorem 0FPWF7TTMB
- Convergence of random variables 0FQ968YKA1
- Meagre set 0FQPYAY9PJ
- Maximum likelihood estimation 0FREPFKNS7
- Identity function 0FSNQ0GNCC
- Order of quantifiers 0FYQMKFE77
- Completion of a metric space 0G4J7Z7WPJ
- Multivariate normal distribution 0G558GJQMW
- Closed set 0G5AV9Q4RR
- Lexicographic order 0G77XFBV00
- Mutual independence of events 0GCVEV6BJA
- Separable space 0GKJ78948V
- Antichain 0GNGPF7KS5
- Chain 0GP9ASVQ1X
- Cardinality of the power set 0GPFKS96T7
- Skewness 0GQ3H7VW3V
- Pseudometric space 0H3W614GEC
- Disjunction 0H5GKDTB01
- Upper bound 0H5J02P8S9
- Galton–Watson process 0H631CZP5K
- Interior is the largest open subset 0HAZEFH137
- Markov property 0HB8SXHPFA
- Limit point 0HBQC2GJXT
- Intersection 0HBRW4E6G1
- Zermelo–Fraenkel set theory 0HE5WDQ9FJ
- Union of open sets is open 0HEF46RPEK
- Russell's paradox 0HESMMSYEG
- First-countable space 0HG11FW8MJ
- Axiom of choice 0HTGB13FE2
- Injective iff it has a left inverse 0HYFEEZAEM
- Student's t-test 0HYP606RYF
- Proof by contradiction 0J0XBKG64S
- Equivalent norms 0J3578562S
- Associativity of composition 0J6AKYZQT8
- Discrete random variable 0J6Z6H5VQJ
- Bernoulli distribution 0J97P5KZY0
- Converse relation 0JCSQNNP2M
- Convergence in distribution 0JDAQHWA9N
- The cumulative distribution function determines the distribution 0JEVZAFDY6
- Regular space 0JF9KW2TXB
- Boundary 0JJ9J1XZ8G
- Sample variance 0JN9P4A944
- Cardinality 0JTGRV4WT4
- Tychonoff's theorem 0JTRSJKCFB
- Existential quantifier 0JW2FHW7G3
- Bayesian inference 0JWRJX2RMP
- Path-connected space 0K0GE6BCYW
- Topologist's sine curve 0K3T4A659R
- Confidence interval 0K4NMMJBG2
- Complement of an open set is closed 0K67Q60Z8P
- Compactness and sequential compactness agree in metric spaces 0K8SGQSV7G
- Continuous image of a compact set is compact 0K9AAJ8G51
- Venn diagram 0KCT6DPXJK
- Posterior probability 0KJ7ZS8AJA
- Hausdorff maximal principle 0KM4KVR9MV
- p-norm on R^n 0KNJWEVSMG
- Nowhere dense set 0KSM23SN3H
- Variance under scaling 0KVQ9D86BM
- Discrete uniform distribution 0KYP951QWH
- Conjunction 0M28ASWG8T
- Universal property of the product topology 0M6W4XNST6
- Epsilon characterisation of Cauchy sequences 0MCK8K2D7Z
- Minimal element 0MCR8ZAXQD
- One-point compactification 0MM45BT6HC
- Continuum hypothesis 0MN2MER9WN
- Compact Hausdorff spaces are normal 0MQQQ5NA2S
- Contraction mapping 0MT2S0ZX4Y
- Equicontinuity 0MW2WXTHMC
- Hausdorff space 0MXB4CKHFW
- Coupon collector's problem 0MXCP7MXWJ
- Cumulative distribution function 0MXMS3AE13
- Open connected subsets of R^n are path-connected 0MXN7AFBPE
- Characteristic function 0MYDNRT7PP
- Compact subsets of a Hausdorff space are closed 0MYFJVMN7M
- Well-ordering theorem 0N109NG5ZX
- Completeness via Cauchy sequences 0N1ZWFJDN5
- Uniqueness quantifier 0N3ADS4CHH
- Hilbert's hotel 0N3Y8G340X
- Pairwise independence 0N57D1XY6T
- Symmetric relation 0N9SA25Z3V
- Cauchy distribution 0NA6Q82YR7
- Double negation law 0NFAGWH84K
- Bayes' theorem 0NM6E9VW04
- Variance as the mean of the square minus the square of the mean 0NMF95YK8W
- Epsilon-net characterisation of total boundedness 0NMGJJ19HD
- Birthday problem 0NMWG2PHJ0
- Moment-generating function 0NNRNGKMFM
- Cantor pairing function 0NP5N5PYW5
- Student's t-distribution 0NQ5798SB1
- Connected components are closed 0NRT0E2QT2
- Characteristic function of the normal distribution 0NS0TDA4E2
- Direct proof 0NTF6DMVAP
- Open cover 0NVPNC12JY
- Second Borel–Cantelli lemma 0NWXRAMEE7
- Sum of independent normal random variables 0NXGPJWNFN
- Closed map 0NYZ2M45G9
- Independence of two events 0P0MZ4X682
- Negation of a universal statement 0P3A06QNDP
- Compactness via open covers 0P6PMJB4MA
- Linearity of expectation 0P7PTC8DDE
- Bounded set 0P953MG05E
- Metric spaces are Hausdorff 0P9DCDES73
- Sup norm on bounded continuous functions 0PARCKE8WP
- Monty Hall problem 0PBWWQD9KY
- Transitive closure 0PEJH7AC74
- Moment 0PH0VHTQS0
- Heine–Borel theorem in finite-dimensional normed spaces 0PHT6NBYPB
- Projections are continuous 0PM88Z9W4M
- Interior is open 0PNWCM559P
- Beta distribution 0PP5ZAJPP7
- Probability of the complement 0PQEBTYDZM
- Expectation with respect to the binomial distribution 0PVCTCKD3C
- Injective function 0PVG1CRAJN
- Cumulant generating function 0Q2QC81VTW
- Image of a set 0Q3F20XB0A
- Joint probability distribution 0QAR0XDZH4
- Probability distribution 0QB913WM5E
- Equivalence relation induced by a function 0QE5PFJY7V
- Stochastic process 0QH5ENKZM1
- Cardinal number 0QKPNZKNEA
- Sample mean 0QNRBHWV35
- Compact space 0QPHW703PV
- Connected set 0R37DFJKFW
- T0 space 0R3B7DX55J
- Type I and type II errors 0R41PVFA39
- Almost surely 0R46A1XY60
- Compact subsets of a metric space are bounded 0R7BTEWCJ2
- Ordinal number 0RDJK7EQYY
- Generating function of a sum of independent random variables 0REMT01N36
- Chi-squared distribution 0RFMMBHFTV
- Limit of the cumulative distribution function at infinity 0RJ5TZH6G0
- Cantor set is homeomorphic to the space of binary sequences 0RQ8DHHR8V
- Converse 0RVYE75E2M
- Every infinite set has a countably infinite subset 0RWQ5VZ6VQ
- Image of an intersection 0RX7DDBYCK
- Preorder 0RXS8R6K37
- Law of excluded middle 0RYYK8PG4S
- Continuous linear map 0S3SMRH0Z5
- Path component 0SB9FNZECG
- Countably infinite set 0SEZ3JGZP7
- Equivalence relation 0SGTMBEWRF
- Closure is the smallest closed superset 0SHC6Z304Z
- Bijective function 0SNQEF7Z53
- Hypergeometric distribution 0SPBPW3K61
- Open map 0SQ2PC596Y
- Moments are derivatives of the moment-generating function at zero 0STK8KEY9G
- Almost sure convergence implies convergence in probability 0SVN6X695K
- Continuous map of topological spaces 0SY9ECQ19Q
- Bertrand paradox 0T0JWJ3M47
- Least element 0T2NTJCV83
- Subspace metric 0T2WYDTRP2
- Predicate 0T3DPBG981
- First Borel–Cantelli lemma 0T6WS7TT77
- The characteristic function determines the distribution 0T8BYAFEXX
- Axiom of extensionality 0TB16T2C97
- Lipschitz map 0TMZ21WKCN
- Set-builder notation 0TMZ89Q5KA
- Law of a random variable 0TST4MHA3A
- Convergence in mean 0TTA57SEJG
- Estimator 0TTNRP5PFQ
- Equivalent metrics 0TWQ5PRKWS
- Surjective iff it has a right inverse 0TYQNHVB4C
- Maximal element 0TZEEFTNCC
- Variance of a sum of independent random variables 0V0778DCW9
- Aleph-null 0V2H5PGJ9B
- Continuous real function on a compact set attains its bounds 0V4DET59NW
- Vacuous truth 0V4QXPGJQK
- Mean squared error 0V4VSCBXP3
- Biconditional 0V6GAWTBYW
- Quotient topology 0V8046R0P9
- Poisson distribution 0VEFSSKX18
- Probability measure 0VGMEBVW1M
- Continuity is equivalent to sequential continuity in metric spaces 0VGPKZ8MRK
- De Morgan's laws for sets 0VK0W4D5Y5
- Banach fixed point theorem 0VK6VEH345
- Isometric isomorphism 0VRD8GC5BM
- Binomial distribution 0VRWZDWW6B
- Indicator function 0VSB0XF4G7
- Standard deviation 0VTN5RKNC5
- Compact closed unit ball implies finite dimension 0VZVV8VME5
- Complete subspaces are closed 0W41XG4W60
- Disjoint sets 0W4RPA8QH3
- Law of total probability for an event and its complement 0W62TKMW7V
- Inverse function 0W766JAPSN
- Cardinality of the continuum 0WC28W9DNM
- Proof by cases 0WCP0PVET6
- Totally bounded set 0WE5BBHGM6
- Probability mass function 0WF4EJP91W
- Monotone function 0WFF6AZPBP
- Gambler's ruin 0WFMKK7DFZ
- Continuous uniform distribution 0WGDPYR30Q
- Circle as a quotient of the real line 0WH1GVBJNH
- Hoeffding's inequality 0WPDNXGSSN
- Moment-generating function of a sum of independent random variables 0WRZ170YEH
- Cantor's theorem 0WTEMGYV2C
- Hölder continuity 0WZTM0EFR6
- Countable intersection of dense open sets is dense 0X2T63GFQQ
- Tietze extension theorem 0X52TNMTCJ
- Uncountable set 0X55M9XET4
- Continuity of probability measures 0X8HBKCSYB
- Independence of random variables 0XCE070V8B
- Cantor's diagonal argument 0XCH8QVDCQ
- Geometric distribution 0XCVV5Q500
- Monotonicity of the cumulative distribution function 0XD22PBMWA
- Reflexive relation 0XEGNW851S
- Function 0XHDTE5YMZ
- Consistent estimator 0XJVF81QF6
- Surjective function 0XKH881BZ7
- Poisson limit theorem 0XKTZRWTXX
- Negative binomial distribution 0XN7KEVSSS
- Negation 0XR7A7RSXB
- Graph of a function 0Y0KFHF47G
- Modus ponens 0Y0MQYST0M
- Tail sum formula for expectation 0Y6QNF1J49
- Order isomorphism 0Y74KN99A5
- Conditional expectation 0YAMJRK04E
- Absorbing Markov chain 0YB93GWTKK
- Comparability of cardinals 0YBHSJMN3J
- Continuity via open sets 0YF82GBTND
- Sum of independent Poisson random variables 0YH1M56SBN
- Closed balls are closed 0YS40B38JD
- Conditional probability distribution 0YVDC5PYDW
- Choice function 0YXEQWRGP0
- Symmetric difference 0Z49NTR1DZ
- Proper metric space 0Z4V98VN5E
- Product topology 0Z57EC6YX3
- Greatest element 0Z7HDDXX3X
- Countable union of countable sets is countable 0Z8FM54P86
- Probability-generating function 0Z8PSSAVBA
- Memorylessness 0ZAZZ34WQS
- Countable set 0ZG61TFBES
- Transfinite induction 0ZHQMQ2C1N
- Conditional independence 0ZJ87ZZ8PK
- Path-connected spaces are connected 0ZMT1GP4KM
- Implication 0ZNX6DQ3EJ
- Central moment 0ZT24EC90K
- Operator norm 0ZTEH055YF
- Law of large numbers 0ZVEAYVRC3
- Quotient set 0ZVHXDSZC7
- Probability space 0ZYBZ34RT2
Sources
- Web https://en.wikipedia.org/wiki/Proposition, lead section
What links here
Used by
- Propositional logic 09K9MWD2QQ
- Disjunction 0H5GKDTB01
- Conjunction 0M28ASWG8T
- Predicate 0T3DPBG981
- Negation 0XR7A7RSXB
- Implication 0ZNX6DQ3EJ