Mathematical logic and foundations Definition
Power set
Builds on Subset
Remarks
Other notations are and . Example: . A finite set with elements has a power set with elements. See cardinality of the power set. By Cantor's theorem, no set is in bijection with its power set.
Reading path
To understand this page from the ground up, read these 8 pages in order. The foundations come first.
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- no evidence level
- Element definition
- Proposition concept
- Set definition
- Implication definition
- Predicate definition
- Universal quantifier definition
- Subset definition
- Power set definition
Where this leads
410 pages build on this one.
- Variance
- Prior probability
- Event
- Chernoff bound
- Chapman–Kolmogorov equation
- Bias of an estimator
- Identically distributed random variables
- Law of the unconscious statistician
- Density of the normal distribution
- Exponential distribution
- Covariance matrix
- Chebyshev's inequality
- Characteristic function of a sum of independent random variables
- Stationary distribution
- Bernoulli process
- Markov chain
- Statistic
- Law of total variance
- Variance of the normal distribution
- Cauchy–Schwarz inequality for expectations
- Monotonicity of probability
- Correlation coefficient
- Variance under translation
- Almost sure convergence
- Law of total expectation
- Sigma-algebra
- Probability density function
- Expectation of a product of independent random variables
- Likelihood function
- Markov's inequality
- Standard score
- Poisson point process
- Gamma distribution
- De Moivre–Laplace theorem
- Buffon's needle problem
- Kolmogorov's zero–one law
- The reals have the cardinality of the continuum
- Independent random variables are uncorrelated
- Convolution of probability distributions
- Normal distribution
- Mean of the Poisson distribution
- Statistical hypothesis test
- Independence means the joint law is the product of the marginals
- Median
- Geometric probability
- Dirac measure
- Method of moments
- Mean of the normal distribution
- Independent sigma-algebras
- Independent and identically distributed random variables
- Classical definition of probability
- Pairwise independent events that are not mutually independent
- Marginal distribution
- Moment-generating function of the normal distribution
- Quantile function
- Weak law of large numbers
- Multiplication rule
- Borel sigma-algebra
- Addition rule for two events
- Random walk
- Random variable with a density
- Uncorrelated random variables that are not independent
- Kurtosis
- Martingale
- Variance of a sum
- Probability axioms
- Mean of the geometric distribution
- Expected value
- Strong law of large numbers
- Covariance
- Random variable
- Base rate fallacy
- Law of total probability
- Independence of two random variables
- Neyman–Pearson lemma
- Convergence in probability
- Boole's inequality
- P-value
- Chi-squared test
- Convergence in probability implies convergence in distribution
- Central limit theorem
- 68–95–99.7 rule
- Transition matrix
- Conditional variance
- Conditional probability
- Lévy's continuity theorem
- Convergence of random variables
- Maximum likelihood estimation
- Multivariate normal distribution
- Mutual independence of events
- Cardinality of the power set
- Skewness
- Galton–Watson process
- Markov property
- Student's t-test
- Discrete random variable
- Bernoulli distribution
- Convergence in distribution
- The cumulative distribution function determines the distribution
- Sample variance
- Bayesian inference
- Confidence interval
- Posterior probability
- Variance under scaling
- Discrete uniform distribution
- Continuum hypothesis
- Coupon collector's problem
- Cumulative distribution function
- Characteristic function
- Pairwise independence
- Cauchy distribution
- Bayes' theorem
- Variance as the mean of the square minus the square of the mean
- Birthday problem
- Moment-generating function
- Student's t-distribution
- Characteristic function of the normal distribution
- Second Borel–Cantelli lemma
- Sum of independent normal random variables
- Independence of two events
- Linearity of expectation
- Monty Hall problem
- Moment
- Beta distribution
- Probability of the complement
- Expectation with respect to the binomial distribution
- Cumulant generating function
- Joint probability distribution
- Probability distribution
- Stochastic process
- Sample mean
- Type I and type II errors
- Almost surely
- Generating function of a sum of independent random variables
- Chi-squared distribution
- Limit of the cumulative distribution function at infinity
- Hypergeometric distribution
- Moments are derivatives of the moment-generating function at zero
- Almost sure convergence implies convergence in probability
- Bertrand paradox
- First Borel–Cantelli lemma
- The characteristic function determines the distribution
- Law of a random variable
- Convergence in mean
- Estimator
- Variance of a sum of independent random variables
- Mean squared error
- Poisson distribution
- Probability measure
- Binomial distribution
- Standard deviation
- Law of total probability for an event and its complement
- Cardinality of the continuum
- Probability mass function
- Gambler's ruin
- Continuous uniform distribution
- Hoeffding's inequality
- Moment-generating function of a sum of independent random variables
- Cantor's theorem
- Continuity of probability measures
- Independence of random variables
- Geometric distribution
- Monotonicity of the cumulative distribution function
- Consistent estimator
- Poisson limit theorem
- Negative binomial distribution
- Tail sum formula for expectation
- Conditional expectation
- Absorbing Markov chain
- Sum of independent Poisson random variables
- Conditional probability distribution
- Probability-generating function
- Memorylessness
- Conditional independence
- Central moment
- Law of large numbers
- Probability space
- Doob's upcrossing inequality
- Bernstein–von Mises theorem
- Cramér–Rao bound
- Efficiency of an estimator
- Log-rank test
- Functional data analysis
- Poisson regression
- Sequential analysis
- Ergodic decomposition
- Koksma–Hlawka inequality
- Hodges' superefficient estimator
- Martingale representation theorem
- Mathematical statistics
- F-test
- Laplace transform of the Dirac delta
- Stationary process
- Orthogonal polynomials on the unit circle
- Cramér–Wold theorem
- Boolean model
- Von Neumann universe
- Stochastic partial differential equation
- Wald–Wolfowitz optimality of the sequential probability ratio test
- Doob's martingale inequality
- Sequential probability ratio test
- Brownian bridge
- Consistency of the maximum likelihood estimator
- Wiener process
- Empirical Bayes method
- Woodin cardinal
- Karhunen–Loève theorem
- Itô isometry
- Naive set theory
- Bayes factor
- Pickands–Balkema–De Haan theorem
- Skolem's paradox
- Dynkin system
- Basu's theorem
- Variogram
- Robbins–Monro algorithm
- Contiguity of measures
- Order statistic
- Dirichlet process
- Lindley's paradox
- Universally measurable set
- M-estimator
- Kunen's inconsistency theorem
- Ornstein–Uhlenbeck process
- Kernel regression
- Bayes estimator
- Adapted process
- Score test
- Kingman's subadditive ergodic theorem
- Multivariate analysis of variance
- McDiarmid's inequality
- Lévy's characterization of Brownian motion
- Asymptotic normality of the maximum likelihood estimator
- Mann–Whitney U test
- Kolmogorov automorphism
- Singular cardinals hypothesis
- Score
- F-distribution
- Edgeworth expansion
- Crofton formula
- Monotone likelihood ratio
- Sample mean and sample covariance
- Wilcoxon signed-rank test
- Moore family
- Metropolis–Hastings algorithm
- Continuous-time Markov chain
- Kriging
- Identifiability
- Baire function
- Minimal sufficient statistic
- Pi-system
- Whittle likelihood
- Logistic regression
- Convergence to equilibrium of ergodic Markov chains
- Cramér–von Mises criterion
- Azuma's inequality
- Gaussian free field
- Parry measure
- Kernel density estimation
- Algebra of sets
- Erdős–Kac theorem
- Detailed balance
- Coupling from the past
- Robust statistics
- Hidden Markov model
- Finite-dimensional distributions
- Continuous mapping theorem
- Bias–variance decomposition
- Lévy process
- Wald's equation
- Random ordinary differential equation
- Monte Carlo integration
- Time series
- Optional stopping theorem
- Measurable space
- Breakdown point
- Delta method
- Minimum description length
- Noncentral chi-squared distribution
- Hájek–Le Cam convolution theorem
- Harmonic measure
- Behrens–Fisher problem
- Cohen's independence of CH
- Submartingale
- Hodges–Lehmann estimator
- Kruskal–Wallis test
- Stochastic difference equation
- Sampling distribution
- Information geometry
- Recurrence and transience of states
- Malliavin calculus
- Wishart distribution
- Birth–death process
- Bayes risk
- Statistical inference
- Minimum-variance unbiased estimator
- Sign test
- Slutsky's theorem
- Tanaka's formula
- Geometric Brownian motion
- Empirical likelihood
- Dvoretzky–Kiefer–Wolfowitz inequality
- Bayesian information criterion
- Berry–Esseen theorem
- Continuity of measure from below and above
- Hunt process
- Cochran's theorem
- Stochastic approximation
- Jackknife
- Quantile regression
- Markov chain mixing time
- Birkhoff's ergodic theorem
- Akaike information criterion
- Set theory
- Hewitt–Savage zero–one law
- Jensen's inequality for integrals
- Statistical model
- Reflection principle
- Credible interval
- Conformal modulus
- Proper forcing axiom
- Independence of sample mean and sample variance for normal samples
- Self-similar process
- Gibbs sampling
- Estimating equations
- Supermartingale
- Anderson–Darling test
- Spearman's rank correlation coefficient
- Family-wise error rate
- Markov chain Monte Carlo
- Dickey–Fuller test
- Generalized method of moments
- Doob's martingale convergence theorems
- Random integral equation
- Uniformly most powerful test
- Bernstein inequalities
- Kendall rank correlation coefficient
- Semimartingale
- Empirical distribution function
- Bootstrap
- Lawvere's fixed-point theorem
- Influence function
- Oseledets theorem
- Itô calculus
- Ancillary statistic
- Stopped process
- Jeffreys prior
- Moments of the log-normal distribution
- Complete statistic
- Horvitz–Thompson estimator
- U-statistic
- Fractional Brownian motion
- Bayesian hierarchical model
- L-estimator
- Power of a test
- Parametric model
- Gödel's consistency of CH and AC
- Randomization
- Sufficient statistic
- Gaussian process
- Missing data mechanisms
- Likelihood-ratio test
- Cardinal characteristics of the continuum
- Karlin–Rubin theorem
- Erdős–Rado theorem
- Conjugate prior
- Kolmogorov–Smirnov test
- Expectation–maximization algorithm
- Hotelling's T-squared distribution
- Burkholder–Davis–Gundy inequality
- Doob–Meyer decomposition theorem
- Cross-validation
- Barbier's theorem
- Wald test
- Extremal length
- Pivotal quantity
- Generalized linear model
- Random graph
- Von Neumann–Bernays–Gödel set theory
- Box–Jenkins method
- Kolmogorov continuity theorem
- Shrinkage estimator
- Pesin theory
- Empirical process
- Binomial proportion confidence interval
- Lévy's upward theorem
- False discovery rate and the Benjamini–Hochberg procedure
- Particle filter
- Neyman construction
- Easton's theorem
- Wilks' theorem
- Skorokhod's embedding theorem
- Blaschke–Lebesgue theorem
- Permutation test
- Fisher's exact test
- Bonferroni correction
- Doob decomposition theorem
- Local asymptotic normality
- Frequentist inference
- Likelihood principle
- Fisher–Neyman factorization theorem
- Girsanov theorem
- Martin's axiom
- Quadratic variation
- Beth number
- Observed information
- Feller process
- Point estimation
- Local martingale
- Completion of a measure
Further reading
- Web https://en.wikipedia.org/wiki/Power_set, lead section
About this page
| Tag | 0BC7KX51Z8 |
|---|---|
| URI | m2://0BC7KX51Z8 |
| Kind | definition |
| Writing | W1 stated |
| MSC | 03E20 |
| Defines | Power set |
| Uses | Subset |
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What this page needs for W2
- edge instance_of in: one example (0 of 1)
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