2. WHAT IS
INFINITY?
ITS HISTORY
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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[1]
and the infinitesimal calculus,
mathematicians began to work with
infinite series and what some
mathematicians (including l'Hôpital and
Bernoulli)[2] regarded as infinitely small
quantities, but infinity continued to be
associated with endless processes.
3. WHAT IS
INFINITY?
ITS HISTORY
EXAMPLES
OTHER
TOPICS
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INFORMATION
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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.[1] 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.[1][3] For
example, if a line is viewed as the set of all of its points,
their infinite number (i.e., the cardinality of the line) is
larger than the number of integers.[4] In this usage,
infinity is a mathematical concept, and infinite
mathematical objects can be studied, manipulated, and
used just like any other mathematical object.
Ancient cultures had
various ideas about the
nature of infinity.
The ancient
Indians and
the Greeks did not
define infinity in
precise formalism as
does modern
mathematics, and
instead approached
infinity as a
philosophical concept.
5. WHAT IS
INFINITY?
ITS HISTORY
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OTHER
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THE MATHEMATICAL INFINITY
For example, 1 + 1/2 + 1/3 + … is an
infinite series. Infinity is a means to
describe anything that is endless,
making it impossible to measure. It
refers to unending time, a series of
numbers that continues forever, or a
perpetual series of operations.
6. WHAT IS
INFINITY?
ITS HISTORY
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OTHER
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THE PHYSICAL INFINITY
'Physical infinity' moves from
mathematics to the real world
and tackles questions such as 'is
space infinite? ' In many areas of
physics, the presence of an
infinite quantity (often called a
singularity) is construed as a
warning that the theory is losing
touch with reality.
7. WHAT IS
INFINITY?
ITS HISTORY
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OTHER
TOPICS
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INFORMATION
KINDS OR
TYPES
CREDITS
THE METAPHYSICAL INFINITY
Infinity in Physical Science. From
a metaphysical perspective, the
theories of mathematical physics
seem to be ontologically
committed to objects and their
properties. If any of those
objects or properties are infinite,
then physics is committed to
there being infinity within the
physical world.