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The equality 0.999… = 1 has long been taught in textbooks, and in the last few decades, researchers of mathematics education have studied the reception of this equation among students, who often vocally reject the equality. The students' reasoning is often based on an expectation that infinitesimal quantities should exist, that arithmetic may be broken, or simply that 0.999… should have a last 9. These ideas are false with respect to the real numbers, which can be proven by explicitly constructing the reals from the rational numbers, and such constructions can also prove that 0.999… = 1 directly. At the same time, some of the intuitive phenomena can occur in other number systems. There are even systems in which an object that can reasonably be called "0.999…" is strictly less than 1.

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Pyrohiv (Ukrainian: Пирогів), also known as Pirogovo (Russian: Пирого́во), originally a village south of Kiev, is a neighborhood in the southern outskirts of the Ukrainian capital city. It is now home to an outdoor Museum of Folk Architecture and Life of Ukraine.
Although the origin of the toponym is uncertain, pyrohiv (gen. pl.) is a Ukrainian word meaning a kind of pastry.Museum

Wooden church at the Pyrohiv Museum
The territory of historic Pyrohiv now serves as the location of a 150-Hectare (370 acre) outdoor Museum of Folk Architecture and Life of Ukraine. Founded in 1969, the museum contains over 300 pieces of folk architecture brought here from all parts of Ukraine and carefully reassembled. The picturesque hill with several windmills is the museum centerpiece and the entire territory of the museum is divided into sectors, each representing the folk architecture and life of a specific Ukrainian region.
Commoner's homes, buildings of small trade, commerce and local administration, and old wooden village churches contain authentic items that represent the everyday lifestyle of Ukrainian villagers and townsfolk. Local volunteers and modern Ukrainian artisans selling their wares dress in old-style clothes and demonstrate the use of authentic everyday items to visitors.
Pyrohiv museum has been accorded the status of State Museum of Ukraine and is affiliated with the Institute of Arts, Folklore and Ethnology of the National Academy of Science of Ukraine.
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Recent controversies

Fire safety is a significant concern as most of the museum's structures are wooden, and many houses have thatched roofs.
In recent years, several of the museum's wooden buildings were damaged by fires. The most recent fire on September 15, 2006 completely destroyed one house and heavily damaged two others. According to both Institute Director Hanna Skrypnyk and the Ukrainian Ministry of Emergencies, the fire was the result of arson, set to cover up the theft of a valuable collection of eighteenth-century cassones which were exhibited in the burned building. Skrypnyk noted that in Soviet times the museum had a designated security group and fire house, which were disbanded after the Soviet collapse owing to negligence in financing on the part of the Ukrainian government.
The land usage in the vicinity of the museum has become the center of scandal as the local authorities approved several commercial construction projects, including a luxurious high-rise entertainment complex and a gasoline filling station. The building construction is now stalled due to the public outrage but the filling station construction near the museum entrance has proceeded.

The entrance to the museum

The windmill

The beehive

The church and beehives