Group - Mathematics

Mathematics

  • Group (mathematics), a set together with a binary operation satisfying certain algebraic conditions
    • Group theory, the study of groups
    • Group action, a way of describing the symmetries of objects using groups
    • Group isomorphism, a one-to-one correspondence (function) between two groups which respects the given group operations
    • Group object, a kind of generalization of a group which is built on more complicated structures than sets

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Famous quotes containing the word mathematics:

    Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.
    Walter Reisch (1903–1963)

    Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
    Simone Weil (1909–1943)