Universal set
Definition
In a given context, fix a set such that all the sets under discussion are subsets of . The set is then the universal set, or the universe of discourse, of the context.
Remarks
In elementary number theory, can be the set of integers. The complement of a set is taken relative to the universal set. In Zermelo–Fraenkel set theory, no set contains all sets. This is a consequence of Russell's paradox.
Explanations
L1 human
The universal set is the "whole world" of a problem. In a problem about real numbers, it is . In a Venn diagram, it is the rectangle that contains all the circles.
What this node needs for W2
- edge instance_of in: one example (0 of 1)
- edge not_instance_of in: one non-example that fails one clause (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
236 nodes use this node, directly or through other nodes.
- Closure is the set of limits of sequences 003QP7A8HG
- Variance 007QED3E0Y
- Finite intersection property 00BWV5CKCF
- Prior probability 00NBBSXRQS
- Event 00SQGJNRTB
- Chernoff bound 014PEBGDYF
- Chapman–Kolmogorov equation 01APZ8GDQH
- Bias of an estimator 01BD2TFFP4
- Totally disconnected space 01CYW8S04D
- Urysohn's lemma 01EY3VR7ZD
- Cantor set is closed 01VT24J1SD
- Identically distributed random variables 01X8YSDTBW
- Law of the unconscious statistician 01ZWX875AT
- Density of the normal distribution 027JF1FBB0
- Exponential distribution 028Z8WC5Y9
- Covariance matrix 02CBHV4ZZQ
- Chebyshev's inequality 02HZ1BK3MW
- Characteristic function of a sum of independent random variables 02JGYG0T7M
- Stationary distribution 02KYGSCTCN
- Closure is closed 02TZDKG50Q
- Bernoulli process 02XPXR1FBK
- Markov chain 033TJBZDG0
- Statistic 036756NFD6
- 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
- Continuous bijection from a compact space to a Hausdorff space is a homeomorphism 0430ETCMKD
- Monotonicity of probability 0464Z0JP2E
- Correlation coefficient 04CTY6XYWN
- Variance under translation 04CYN5G6RY
- Almost sure convergence 04P7D63W8P
- Law of total expectation 04RRB6HM00
- Sigma-algebra 04WSW8T3SY
- Probability density function 04YG690N5V
- Expectation of a product of independent random variables 05AW1G0WE1
- Likelihood function 05FSTXM92W
- T1 space 05GQJXBP3F
- Markov's inequality 05PWWHYBX5
- Standard score 05RZ4YZG4E
- Poisson point process 05TG0SE4HT
- Gamma distribution 06395GBNWD
- De Moivre–Laplace theorem 065X9S8CM3
- Closed subsets of compact sets are compact 066HW6D9A7
- Closure in a metric space 068P0P32DW
- Buffon's needle problem 06X5PF6YFP
- Kolmogorov's zero–one law 073Q8Z94KG
- Independent random variables are uncorrelated 077GN9HDR6
- Convolution of probability distributions 07CHJ5YX28
- Heine–Borel theorem 07PFYV65MB
- Normal distribution 07RXBVTVZB
- Mean of the Poisson distribution 086HEVXR9Z
- Statistical hypothesis test 087P03NEND
- Sequence spaces lp 08P6T2WH6R
- Independence means the joint law is the product of the marginals 08QCA2F1NX
- Median 08W2CW8PKW
- Geometric probability 0924BCD257
- Riesz's lemma 097C7KCAT5
- Intermediate value theorem for connected spaces 098C0KZZAP
- Dirac measure 099SXAG014
- Closed sets contain their limits 09GQ3ZTQJ9
- Method of moments 09J1H07VAH
- Mean of the normal distribution 09PR1V6RWR
- Independent sigma-algebras 09T8ZHST1V
- Intersection of closed sets is closed 09YMV8H4X5
- Baire category theorem 0A7KGAYHGV
- 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
- Quantile function 0B3Q3XDM5X
- Continuity via closed sets 0B8GPXFSP7
- Connected subsets of the real line are intervals 0B9ZQFMQNV
- Weak law of large numbers 0BFDHF2H7N
- 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
- Uncorrelated random variables that are not independent 0C6J8BQXVR
- Kurtosis 0CBQVVNBMP
- Martingale 0CDVK9RQBH
- Dense set 0D198GPMTJ
- A set is closed iff it equals its closure 0D2W7FS52T
- Baire space 0D5KR33H7X
- Variance of a sum 0D86GJEZ39
- Connected space 0D939CMME7
- Probability axioms 0DAX8PMAJ4
- Mean of the geometric distribution 0DB0R4N5XX
- Expected value 0DCT0QZVQ1
- Strong law of large numbers 0DFWHQ839T
- Covariance 0DJ8W3HP2D
- Random variable 0DKRR22AEQ
- Closure 0DRKT1QJR7
- Base rate fallacy 0E44JMG6NV
- Law of total probability 0E5G5FMT2R
- Independence of two random variables 0E9502NT92
- Neyman–Pearson lemma 0EE19CFEEF
- Convergence in probability 0EFDDXTVD6
- Boole's inequality 0EGSEE9J9R
- P-value 0EHYZFZ4PK
- 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
- 68–95–99.7 rule 0EYQ03XCR3
- Cantor's intersection theorem 0EZBG8SKJM
- Transition matrix 0F1KBVY161
- Conditional variance 0F1SN93KXE
- Closed subsets of complete spaces are complete 0FBXJZX3MK
- Conditional probability 0FJB06AD2P
- Lévy's continuity theorem 0FPWF7TTMB
- Convergence of random variables 0FQ968YKA1
- Meagre set 0FQPYAY9PJ
- Maximum likelihood estimation 0FREPFKNS7
- Completion of a metric space 0G4J7Z7WPJ
- Multivariate normal distribution 0G558GJQMW
- Closed set 0G5AV9Q4RR
- Mutual independence of events 0GCVEV6BJA
- Separable space 0GKJ78948V
- Skewness 0GQ3H7VW3V
- Galton–Watson process 0H631CZP5K
- Markov property 0HB8SXHPFA
- Student's t-test 0HYP606RYF
- Discrete random variable 0J6Z6H5VQJ
- Bernoulli distribution 0J97P5KZY0
- Convergence in distribution 0JDAQHWA9N
- The cumulative distribution function determines the distribution 0JEVZAFDY6
- Regular space 0JF9KW2TXB
- Boundary 0JJ9J1XZ8G
- Sample variance 0JN9P4A944
- Bayesian inference 0JWRJX2RMP
- Topologist's sine curve 0K3T4A659R
- Confidence interval 0K4NMMJBG2
- Complement of an open set is closed 0K67Q60Z8P
- Venn diagram 0KCT6DPXJK
- Posterior probability 0KJ7ZS8AJA
- p-norm on R^n 0KNJWEVSMG
- Nowhere dense set 0KSM23SN3H
- Variance under scaling 0KVQ9D86BM
- Discrete uniform distribution 0KYP951QWH
- One-point compactification 0MM45BT6HC
- Compact Hausdorff spaces are normal 0MQQQ5NA2S
- 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
- Pairwise independence 0N57D1XY6T
- Cauchy distribution 0NA6Q82YR7
- Bayes' theorem 0NM6E9VW04
- Variance as the mean of the square minus the square of the mean 0NMF95YK8W
- Birthday problem 0NMWG2PHJ0
- Moment-generating function 0NNRNGKMFM
- Student's t-distribution 0NQ5798SB1
- Connected components are closed 0NRT0E2QT2
- Characteristic function of the normal distribution 0NS0TDA4E2
- Second Borel–Cantelli lemma 0NWXRAMEE7
- Sum of independent normal random variables 0NXGPJWNFN
- Closed map 0NYZ2M45G9
- Independence of two events 0P0MZ4X682
- Linearity of expectation 0P7PTC8DDE
- Monty Hall problem 0PBWWQD9KY
- Moment 0PH0VHTQS0
- Heine–Borel theorem in finite-dimensional normed spaces 0PHT6NBYPB
- Beta distribution 0PP5ZAJPP7
- Probability of the complement 0PQEBTYDZM
- Expectation with respect to the binomial distribution 0PVCTCKD3C
- Cumulant generating function 0Q2QC81VTW
- Joint probability distribution 0QAR0XDZH4
- Probability distribution 0QB913WM5E
- Stochastic process 0QH5ENKZM1
- Sample mean 0QNRBHWV35
- Connected set 0R37DFJKFW
- Type I and type II errors 0R41PVFA39
- Almost surely 0R46A1XY60
- 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
- Closure is the smallest closed superset 0SHC6Z304Z
- Hypergeometric distribution 0SPBPW3K61
- Moments are derivatives of the moment-generating function at zero 0STK8KEY9G
- Almost sure convergence implies convergence in probability 0SVN6X695K
- Bertrand paradox 0T0JWJ3M47
- First Borel–Cantelli lemma 0T6WS7TT77
- The characteristic function determines the distribution 0T8BYAFEXX
- Law of a random variable 0TST4MHA3A
- Convergence in mean 0TTA57SEJG
- Estimator 0TTNRP5PFQ
- Variance of a sum of independent random variables 0V0778DCW9
- Continuous real function on a compact set attains its bounds 0V4DET59NW
- Mean squared error 0V4VSCBXP3
- Poisson distribution 0VEFSSKX18
- Probability measure 0VGMEBVW1M
- De Morgan's laws for sets 0VK0W4D5Y5
- Binomial distribution 0VRWZDWW6B
- Standard deviation 0VTN5RKNC5
- Compact closed unit ball implies finite dimension 0VZVV8VME5
- Complete subspaces are closed 0W41XG4W60
- Law of total probability for an event and its complement 0W62TKMW7V
- Probability mass function 0WF4EJP91W
- 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
- Countable intersection of dense open sets is dense 0X2T63GFQQ
- Tietze extension theorem 0X52TNMTCJ
- Continuity of probability measures 0X8HBKCSYB
- Independence of random variables 0XCE070V8B
- Geometric distribution 0XCVV5Q500
- Monotonicity of the cumulative distribution function 0XD22PBMWA
- Consistent estimator 0XJVF81QF6
- Poisson limit theorem 0XKTZRWTXX
- Negative binomial distribution 0XN7KEVSSS
- Tail sum formula for expectation 0Y6QNF1J49
- Conditional expectation 0YAMJRK04E
- Absorbing Markov chain 0YB93GWTKK
- Sum of independent Poisson random variables 0YH1M56SBN
- Closed balls are closed 0YS40B38JD
- Conditional probability distribution 0YVDC5PYDW
- Probability-generating function 0Z8PSSAVBA
- Memorylessness 0ZAZZ34WQS
- Conditional independence 0ZJ87ZZ8PK
- Path-connected spaces are connected 0ZMT1GP4KM
- Central moment 0ZT24EC90K
- Law of large numbers 0ZVEAYVRC3
- Probability space 0ZYBZ34RT2
Sources
- Web https://en.wikipedia.org/wiki/Universal_set, lead section
What links here
Used by
- Complement 0B1FSS1VZW