Diagonalization
... Proof: (by contradiction) Let R denote the set of all real numbers, and suppose that R is countable. Then by definition it is either finite or countably infinite. Clearly, it is not finite, therefore it must be countably infinite. By definition, since it is countably infinite it has the same cardina ...
... Proof: (by contradiction) Let R denote the set of all real numbers, and suppose that R is countable. Then by definition it is either finite or countably infinite. Clearly, it is not finite, therefore it must be countably infinite. By definition, since it is countably infinite it has the same cardina ...
Power Point
... probability theory. Probability theory is used to understand events where all possible outcomes are known in advance, but where it is not possible to predict the actual outcome with certainty. ...
... probability theory. Probability theory is used to understand events where all possible outcomes are known in advance, but where it is not possible to predict the actual outcome with certainty. ...
Algebra Vocabulary
... A set is said to be closed under some operation if the operation on members of the set produces a member of the set. A set that is closed under an operation or collection of operations is said to satisfy a closure property. For example, the real numbers are closed under subtraction, where the subset ...
... A set is said to be closed under some operation if the operation on members of the set produces a member of the set. A set that is closed under an operation or collection of operations is said to satisfy a closure property. For example, the real numbers are closed under subtraction, where the subset ...
2011 GHSGT Math Practice Questions
... 61. Sam is trying to calculate the height of a tower. He is standing 95 meters from the base of a tower. The angle of elevation from Sam's position on the ground to the top of the tower is 35°. Calculate the height of the tower to the nearest tenth of a meter. ...
... 61. Sam is trying to calculate the height of a tower. He is standing 95 meters from the base of a tower. The angle of elevation from Sam's position on the ground to the top of the tower is 35°. Calculate the height of the tower to the nearest tenth of a meter. ...
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Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)