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contribution of infinity in maths

Answer 1

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Infinity

MATHEMATICS

WRITTEN BY: Rudy Rucker

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Hilbert, David: infinite hotel paradox

Hilbert, David: infinite hotel paradox

Learn about David Hilbert's paradox of the “infinite hotel.”

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Infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1657. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical. Mathematical infinities occur, for instance, as the number of points on a continuous line or as the size of the endless sequence of counting numbers: 1, 2, 3,…. Spatial and temporal concepts of infinity occur in physics when one asks if there are infinitely many stars or if the universe will last forever. In a metaphysical discussion of God or the Absolute, there are questions of whether an ultimate entity must be infinite and whether lesser things could be infinite as well.•

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Answer 2

Answer:

A more direct use of infinity in mathematics arises with efforts to compare the sizes of infinite sets, such as the set of points on a line (real numbers) or the set of counting numbers. ... He similarly showed that the set of counting numbers and their doubles (i.e., the set of even numbers) could be paired up.

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