Following this logic, we will see "Wikip" and "Wikipe" and "Wikiped" and "Wikipedi" all the way until we will see "Wikipedia is the best website in the world". Not only that, but we will see it infinite times.
Since the sentence "Wikipedia is the best website in the world" was just any sentence, by using the proof above, one can know "anything" appears an infinite amount of times. Therefore, we know that all of Shakespeare's things will appear. Even the things he threw away, even the thoughts he had at night, and even Hamlet.
This is like how you can find any combination of numbers (example:1829192) in the number pi since it has an infinite amount of random numbers.
The above proof was an example of a Proof by induction.
Ascomycota
Ascomycota is a phylum of fungi (kingdom Fungi). Members are commonly known as the sac fungi. They have a sac, the ascus, which contains four to eight ascospores in the sexual stage.
The structure defines the group and distinguishes it from other fungi. The ascus is a tube-shaped sac, which contains the sexual spores produced by meiosis and which are called "ascospores".
It was used in genetics because it contains the results of crossing-over between chromosomes.
Random variable
A random variable is used in mathematics to study probability theory. It was developed to model the chance of events happening in all kinds of real-life scenarios.
Take two measurable spaces, and name them formula_1 and formula_2. A measurable space is any pair of sets, called formula_3 and formula_4, that follow these rules:
A random variable, named formula_11, is a measurable function from formula_12 to formula_13. This is written formula_14. A random variable is typically represented by capital roman letters such as formula_15, formula_16, formula_17 and formula_18, and can be either discrete (taking on a countable set of values) or continuous (taking on an interval of values).
The set formula_12 is called the sample space. The set formula_20 is called the event space.
Take a probability measure formula_21 on formula_1. Take a set formula_23 in formula_24. Then formula_25 is defined to mean formula_26.
When you roll a dice, 6 events can happen. These events are the different numbers that can show on the dice: 1, 2, 3, 4, 5, or 6.
Here is an example of a random variable. You roll a fair dice once. If the number on the dice is odd, you eat an apple, and if the number is even, you eat an orange. The random variable is the type of fruit that you will eat. Before you roll the dice, you don't know if you will eat an apple or an orange. We can also write this with mathematics:
Take formula_27. Take formula_20 to be the power set of formula_12. Take formula_30. Take formula_24 to be the power set of formula_13. Our random variable follows the even/odd rule from above:
Here formula_34 represents the number on the dice after you roll it. We said the dice is fair. In mathematics, this means formula_35 for formula_36 and formula_37.
The event that you eat an apple is a set in the event space. It is formula_38. The probability that you eat an apple is the probability measure of this set. It is formula_39.
Here is another example. Sometimes a dice is unbalanced. This means that it rolls some numbers more often than others. We can do the same experiment as above, but with an unbalanced dice.
For example, let's say that we use a dice that has been changed in one way: it never rolls the number 5. Then you are less likely to eat an apple, because 5 is an odd number. The random variable is "exactly" the same as before:
This is because end possibilities have not changed. After the dice is rolled, you will eat an apple or an orange. You don't know which. What has changed is the "probability" that you eat an apple or an orange. In mathematics, this means
The event that you eat an apple is "the same set" as for the fair dice. It is formula_38. But this event is now less likely to happen, because the dice cannot roll a 5. In other words, the probability that you eat an apple is "different" than for the fair dice. It is formula_43.
The examples show that a random variable doesn't automatically give probabilities. If we choose formula_44 differently, one random variable can give different probabilities. This can be confusing. For this reason, mathematicians often define a random variable on a probability space. The mathematical notation for this is formula_45. This fixes the probability measure. Then there is no confusion about the probabilities of events.
María Trinidad Sánchez Province
María Trinidad Sánchez is a province of the Dominican Republic. It is in the northeastern part of the country, along the Atlantic coast. Its capital city is Nagua.
It was created on 1958. It was a municipality of the Samaná province before being elevated to the category of province.
"María Trinidad Sánchez" was an aunt of Francisco del Rosario Sánchez, one of the founders of the country. She helped the Dominican soldiers during the first days of the independence from Haiti. She was killed on 27 February 1845 by orders of the first Dominican president, Pedro Santana.
The territory of the province was part of the Duarte province and then it was made a municipality of the Samaná province. In 1958, it was made a province with the name "Julia Molina", after the mother of the dictator Rafael Trujillo, with the municipalities of Julia Molina and Cabrera and the municipal district, later a municipality, of Río San Juan. In 1961, after Trujillo's death, the province was given the present name and the capital was named Nagua.
The municipality of El Factor was created in 1988.
San José de Matanzas was made a municipal district in 1996, Arroyo Salado in 2000, La Entrada and El Pozo in 2001, Las Gordas in 2003 and Arroyo al Medio in 2006.
María Trinidad Sánchez is in the northeast of the country. The province has the Samaná province to the southeast, the Duarte province to the south and west and the Espaillat province to the northwest. The Atlantic Ocean is to the north and east of the province.
In (last national census), there were people living in the María Trinidad Sánchez province, and 74,019 () living in towns and cities. The population density was persons/km².
Its population represents of the total population of the country and the province is ranked as the 20th (out of 31 plus the National District) more populated province.
, the total estimated propulation of the province is 141,331 inhabitants.
The largest city of the province is Nagua, its capital, with a population (in ) of 40,611 inhabitants.
The María Trinidad Sánchez province has a total area of . It has of the area of the Dominican Republic and it is ranked as the 20th (out of 31 plus the National District) largest province.
The altitude of Nagua, provincial capital, is .
The "Cordillera Septentrional" (in English, "Northern mountain range") is in the southern part of the province, going from the northwest to the southeast. The mountains here are not very high, and the mountain range ends in the southeastern part of the province, in a large swamp called "Gran Estero" close to the Samaná province.
Because the mountain range is close to the sea, the rivers are short.
The protected areas in the province are the Natural Scientific Reserve Loma Guaconejo ("Reserva Científica Natural Loma Guaconejo"), the National Park Cabo Francés Viejo and the National Park Gran Laguna.
The climate of the province is a tropical climate, hot most of the year.
There are 4 municipalities and 6 municipal districts (M.D.) in the province. The municipalities and its municipal districts (M.D.) are:
The main economic activities in the province are farming and fishing. In some partes of the province, mainly in the northern parte (Río San Juan and Cabrera), tourism is an important activity because there are many beautiful beaches.
Monseñor Nouel Province