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The Infinite
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflections 1090029
Reflections may refer to: Books and magazines * ''Reflections; or Sentences and Moral Maxims'', a series of books (1665–1678) by François de La Rochefoucauld (writer), François de La Rochefoucauld * Reflections (Sufi literature), ''Reflections'' (Sufi literature), by Idries Shah * ''Reflections'', an alumni publication of Lubbock Christian University * ''Reflections'', a publication of Yale Divinity School * ''Reflections'', an academic journal on writing and public rhetoric published by New City Community Press Film and television Film * Reflections (1964 film), ''Reflections'' (1964 film) or ''Dry Summer'', a Turkish film directed by Metin Erksan * Reflections (1984 film), ''Reflections'' (1984 film), a British drama film directed by Kevin Billington * Reflections (1987 film), ''Reflections'' (1987 film), a Yugoslavian psychological horror film directed by Goran Marković * Reflections (1999 film), ''Reflections'' (1999 film), a British documentary film directed by Pogus Cae ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actual Infinity
In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities as given, actual and completed objects. These might include the set of natural numbers, extended real numbers, transfinite numbers, or even an infinite sequence of rational numbers. Actual infinity is to be contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps. As a result, potential infinity is often formalized using the concept of Limit (mathematics), limit. Anaximander The ancient Greek term for the potential or improper infinite was ''Apeiron (cosmology), apeiron'' (unlimited or indefinite), in contrast to the actual or proper infinite ''aphorismenon''. ''Apeiron'' stands opposed to that which has a ''peras'' (limit). These notions are tod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apeiron (cosmology)
''Apeiron'' (; ) is a Greek word meaning "(that which is) unlimited," "boundless", "infinite", or "indefinite" from ''a-'', "without" and ''peirar'', "end, limit", "boundary", the Ionic Greek form of ''peras'', "end, limit, boundary". Origin of everything The ''apeiron'' is central to the cosmological theory created by Anaximander, a 6th-century BC pre-Socratic Greek philosopher whose work is mostly lost. From the few existing fragments, we learn that he believed the beginning or ultimate reality (''arche'') is eternal and infinite, or boundless (''apeiron''), subject to neither old age nor decay, which perpetually yields fresh materials from which everything we can perceive is derived. ''Apeiron'' generated the opposites (hot–cold, wet–dry, etc.) which acted on the creation of the world (cf. Heraclitus). Everything is generated from ''apeiron'' and then it is destroyed by going back to ''apeiron'', according to necessity. He believed that infinite worlds are generated f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pre-Socratic Philosophy
Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of these early philosophers spanned the workings of the natural world as well as human society, ethics, and religion. They sought explanations based on natural law rather than the Divinity, actions of gods. Their work and writing has been almost entirely lost. Knowledge of their views comes from ''testimonia'', i.e. later authors' discussions of the work of pre-Socratics. Philosophy found fertile ground in the ancient Greek world because of the close ties with neighboring civilizations and the rise of autonomous civil entities, ''polis, poleis''. Pre-Socratic philosophy began in the 6th century BCE with the three Milesian school, Milesians: Thales, Anaximander, and Anaximenes of Miletus, Anaximenes. They all attributed the ''arche'' (a word that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anaximander
Anaximander (; grc-gre, Ἀναξίμανδρος ''Anaximandros''; ) was a pre-Socratic Greek philosopher who lived in Miletus,"Anaximander" in ''Chambers's Encyclopædia''. London: George Newnes, 1961, Vol. 1, p. 403. a city of Ionia (in modern-day Turkey). He belonged to the Milesian school and learned the teachings of his master Thales. He succeeded Thales and became the second master of that school where he counted Anaximenes and, arguably, Pythagoras amongst his pupils. Little of his life and work is known today. According to available historical documents, he is the first philosopher known to have written down his studies, although only one fragment of his work remains. Fragmentary testimonies found in documents after his death provide a portrait of the man. Anaximander was an early proponent of science and tried to observe and explain different aspects of the universe, with a particular interest in its origins, claiming that nature is ruled by laws, just like human soc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of culturally and linguistically related city-states and other territories. Most of these regions were officially unified only once, for 13 years, under Alexander the Great's empire from 336 to 323 BC (though this excludes a number of Greek city-states free from Alexander's jurisdiction in the western Mediterranean, around the Black Sea, Cyprus, and Cyrenaica). In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Roughly three centuries after the Late Bronze Age collapse of Mycenaean Greece, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and the colonization of the Mediterranean Basin. This was followed by the age of Classical G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vedic Period
The Vedic period, or the Vedic age (), is the period in the late Bronze Age and early Iron Age of the history of India when the Vedic literature, including the Vedas (ca. 1300–900 BCE), was composed in the northern Indian subcontinent, between the end of the urban Indus Valley civilisation and a second urbanisation, which began in the central Indo-Gangetic Plain BCE. The Vedas are liturgical texts which formed the basis of the influential Brahmanical ideology, which developed in the Kuru Kingdom, a tribal union of several Indo-Aryan tribes. The Vedas contain details of life during this period that have been interpreted to be historical and constitute the primary sources for understanding the period. These documents, alongside the corresponding archaeological record, allow for the evolution of the Indo-Aryan and Vedic culture to be traced and inferred. The Vedas were composed and orally transmitted with precision by speakers of an Old Indo-Aryan language who had migrate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universe
The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. According to this theory, space and time emerged together ago, and the universe has been expanding ever since the Big Bang. While the spatial size of the entire universe is unknown, it is possible to measure the size of the observable universe, which is approximately 93 billion light-years in diameter at the present day. Some of the earliest cosmological models of the universe were developed by ancient Greek and Indian philosophers and were geocentric, placing Earth at the center. Over the centuries, more precise astronomical observations led Nicolaus Copernicus to develop the heliocentric model with the Sun at the center of the Solar System. In developing the law of universal gravitation, Isaac Newton built upon Copernicus's work as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosophy, German philosopher Christian Wolff (philosopher), Christian Wolff, in ''Cosmologia Generalis''. Religious cosmology, Religious or mythological cosmology is a body of beliefs based on Mythology, mythological, Religion, religious, and Esotericism, esoteric literature and traditions of Cosmogony, creation myths and eschatology. In the science of astronomy it is concerned with the study of the chronology of the universe. Physical cosmology is the study of the observable universe's origin, its large-scale structures and dynamics, and the ultimate fate of the universe, including the laws of science that govern these areas. It is investigated by scientists, such as astronomers and physicists, as well as Philosophy, ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Arithmetic
The operators in elementary arithmetic are addition, subtraction, multiplication, and division. The operators can be applied on both real numbers and imaginary numbers. Each kind of number is represented on a number line designated to the type. Digits Digits are the set of symbols used to represent numbers. In a numeral system, each digit represents a value. The Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the most common set of symbols, and the most frequently used form of these digits is the Western style. A numeral system defines the value of all numbers that contain more than one digit, most often by adding the value of adjacent digits. The Hindu–Arabic numeral system includes positional notation to determine the value of any numeral. In this type of system, the increase in value of an additional digit includes one or more multiplications with the radix value and the result is added to the value of an adjacent digit. For example, with Arabic numerals, the radix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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