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Essence of Arithmetic
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- Snippet from Wikipedia: Arithmetic
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
Arithmetic systems can be distinguished based on the type of number they operate on. Integer arithmetic restricts itself to calculations with positive and negative whole numbers. Rational number arithmetic involves operations on fractions that lie between integers. Real number arithmetic includes calculations with both rational and irrational numbers and covers the complete number line.
Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix arithmetic.
Arithmetic operations form the basis of many branches of mathematics, such as algebra, calculus, and statistics. They play a similar role in the sciences, like physics and economics. Arithmetic is present in many aspects of daily life, for example, to calculate change while shopping or to manage personal finances. It is one of the earliest forms of mathematics education that students encounter. Its cognitive and conceptual foundations are studied by psychology and philosophy.
The practice of arithmetic is at least thousands and possibly tens of thousands of years old. Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE. Starting in the 7th and 6th centuries BCE, the ancient Greeks initiated a more abstract study of numbers and introduced the method of rigorous mathematical proofs. The ancient Indians developed the concept of zero and the decimal system, which Arab mathematicians further refined and spread to the Western world during the medieval period. The first mechanical calculators were invented in the 17th century. The 18th and 19th centuries saw the development of modern number theory and the formulation of axiomatic foundations of arithmetic. In the 20th century, the emergence of electronic calculators and computers revolutionized the accuracy and speed with which arithmetic calculations could be performed.
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Math: Outline of mathematics, Mathematics research, Mathematical anxiety, Pythagorean Theorem, Scientific Notation, Algebra (Pre-algebra, Elementary algebra, Abstract algebra, Linear algebra, Universal algebra), Arithmetic (Essence of arithmetic, Elementary arithmetic, Decimal arithmetic, Decimal point, numeral system, Place value, Face value), Applied mathematics, Binary operation, Classical mathematics, Control theory, Cryptography, Definitions of mathematics, Discrete mathematics (Outline of discrete mathematics, Combinatorics), Dynamical systems, Engineering mathematics, Financial mathematics, Fluid mechanics (Mathematical fluid dynamics), Foundations of mathematics, Fudge (Mathematical fudge, Renormalization), Game theory, Glossary of areas of mathematics, Graph theory, Graph operations, Information theory, Language of mathematics, Mathematical economics, Mathematical logic (Model theory, Proof theory, Set theory, Type theory, Recursion theory, Theory of Computation, List of logic symbols), Mathematical optimization, Mathematician, Modulo, Mathematical notation (List of logic symbols, Notation in probability and statistics, Physical constants, Mathematical alphanumeric symbols, ISO 31-11), Numerical analysis, Operations research, Philosophy of mathematics, Probability (Outline of probability), Statistics, Mathematical structure, Ternary operation, Unary operation, Variable (mathematics), Glossary, Bibliography (Math for Data Science and DataOps, Math for Machine Learning and MLOps, Math for Programmers and Software Engineering), Courses, Mathematics GitHub. (navbar_math - see also navbar_variables)
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