Countable set
Definition
A set is countable when there is an injective function .
Remarks
Equivalently, is finite or countably infinite. A nonempty set is countable exactly when there is a surjection from to it. Some authors use "countable" only for countably infinite sets, and "at most countable" for this notion. Subsets of countable sets are countable.
Explanations
L1 human
A countable set is one that you can list: first element, second element, and so on. The list may stop, or it may go on forever, but each element appears at some finite position.
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
108 nodes use this node, directly or through other nodes.
- Variance 007QED3E0Y
- Second-countable space 00RE1R4W7N
- Chernoff bound 014PEBGDYF
- Chapman–Kolmogorov equation 01APZ8GDQH
- Bias of an estimator 01BD2TFFP4
- Law of the unconscious statistician 01ZWX875AT
- Covariance matrix 02CBHV4ZZQ
- Chebyshev's inequality 02HZ1BK3MW
- Characteristic function of a sum of independent random variables 02JGYG0T7M
- Stationary distribution 02KYGSCTCN
- Bernoulli process 02XPXR1FBK
- Markov chain 033TJBZDG0
- Law of total variance 03BY5XTNA4
- Variance of the normal distribution 03EESZDB9A
- Cauchy–Schwarz inequality for expectations 03PGHKAJG3
- Correlation coefficient 04CTY6XYWN
- Variance under translation 04CYN5G6RY
- Law of total expectation 04RRB6HM00
- The real numbers are uncountable 0518MM6BE1
- Expectation of a product of independent random variables 05AW1G0WE1
- Likelihood function 05FSTXM92W
- Markov's inequality 05PWWHYBX5
- Poisson point process 05TG0SE4HT
- De Moivre–Laplace theorem 065X9S8CM3
- Independent random variables are uncorrelated 077GN9HDR6
- Convolution of probability distributions 07CHJ5YX28
- Mean of the Poisson distribution 086HEVXR9Z
- Product of countable sets is countable 08G4XH86JC
- Method of moments 09J1H07VAH
- Mean of the normal distribution 09PR1V6RWR
- Baire category theorem 0A7KGAYHGV
- Moment-generating function of the normal distribution 0B1G4E21G7
- Weak law of large numbers 0BFDHF2H7N
- Uncorrelated random variables that are not independent 0C6J8BQXVR
- Kurtosis 0CBQVVNBMP
- Martingale 0CDVK9RQBH
- Baire space 0D5KR33H7X
- Variance of a sum 0D86GJEZ39
- Mean of the geometric distribution 0DB0R4N5XX
- Expected value 0DCT0QZVQ1
- Strong law of large numbers 0DFWHQ839T
- Covariance 0DJ8W3HP2D
- The rationals are countable 0DS9KWFDK2
- Neyman–Pearson lemma 0EE19CFEEF
- Chi-squared test 0EN0V3NY20
- Central limit theorem 0EPZC4Z1FC
- 68–95–99.7 rule 0EYQ03XCR3
- Transition matrix 0F1KBVY161
- Conditional variance 0F1SN93KXE
- Lévy's continuity theorem 0FPWF7TTMB
- Convergence of random variables 0FQ968YKA1
- Meagre set 0FQPYAY9PJ
- Maximum likelihood estimation 0FREPFKNS7
- Separable space 0GKJ78948V
- Skewness 0GQ3H7VW3V
- Galton–Watson process 0H631CZP5K
- Markov property 0HB8SXHPFA
- First-countable space 0HG11FW8MJ
- Student's t-test 0HYP606RYF
- Discrete random variable 0J6Z6H5VQJ
- Bernoulli distribution 0J97P5KZY0
- Sample variance 0JN9P4A944
- Bayesian inference 0JWRJX2RMP
- Confidence interval 0K4NMMJBG2
- Variance under scaling 0KVQ9D86BM
- Discrete uniform distribution 0KYP951QWH
- Coupon collector's problem 0MXCP7MXWJ
- Characteristic function 0MYDNRT7PP
- Variance as the mean of the square minus the square of the mean 0NMF95YK8W
- Moment-generating function 0NNRNGKMFM
- Student's t-distribution 0NQ5798SB1
- Characteristic function of the normal distribution 0NS0TDA4E2
- Sum of independent normal random variables 0NXGPJWNFN
- Linearity of expectation 0P7PTC8DDE
- Moment 0PH0VHTQS0
- Expectation with respect to the binomial distribution 0PVCTCKD3C
- Cumulant generating function 0Q2QC81VTW
- Sample mean 0QNRBHWV35
- Generating function of a sum of independent random variables 0REMT01N36
- Chi-squared distribution 0RFMMBHFTV
- Hypergeometric distribution 0SPBPW3K61
- Moments are derivatives of the moment-generating function at zero 0STK8KEY9G
- The characteristic function determines the distribution 0T8BYAFEXX
- Convergence in mean 0TTA57SEJG
- Variance of a sum of independent random variables 0V0778DCW9
- Mean squared error 0V4VSCBXP3
- Poisson distribution 0VEFSSKX18
- Binomial distribution 0VRWZDWW6B
- Standard deviation 0VTN5RKNC5
- Probability mass function 0WF4EJP91W
- Hoeffding's inequality 0WPDNXGSSN
- Moment-generating function of a sum of independent random variables 0WRZ170YEH
- Countable intersection of dense open sets is dense 0X2T63GFQQ
- Uncountable set 0X55M9XET4
- Cantor's diagonal argument 0XCH8QVDCQ
- Geometric distribution 0XCVV5Q500
- 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
- Conditional probability distribution 0YVDC5PYDW
- Countable union of countable sets is countable 0Z8FM54P86
- Probability-generating function 0Z8PSSAVBA
- Memorylessness 0ZAZZ34WQS
- Central moment 0ZT24EC90K
- Law of large numbers 0ZVEAYVRC3
Sources
- Web https://en.wikipedia.org/wiki/Countable_set, lead section
What links here
Used by
- Second-countable space 00RE1R4W7N
- Markov chain 033TJBZDG0
- Product of countable sets is countable 08G4XH86JC
- Baire space 0D5KR33H7X
- Meagre set 0FQPYAY9PJ
- Separable space 0GKJ78948V
- First-countable space 0HG11FW8MJ
- Discrete random variable 0J6Z6H5VQJ
- Uncountable set 0X55M9XET4
- Cantor's diagonal argument 0XCH8QVDCQ
- Countable union of countable sets is countable 0Z8FM54P86