August 17th, 2010
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Infinity
Origin of the concept of Infinity
The word infinity comes from the Latin word, infinitas or “unboundedness.” It refers to various
distinct concepts (usually linked to the idea of “without end” which arise in philosophy, mathematics, and theology).
In mathematics, “infinity” is often used in contexts where it is treated as if it were a number (i.e., it counts or measures
things: “an infinite number of terms”) but it is a different type of “number” when compared to the real numbers.
It was not until the late 19th century that Georg Cantor (1845-1918), a German mathematician, finally described
infinity in a way to do arithmetic with infinite quantities useful to mathematics putting it on a firm logical
foundation. His basic definition was simple: a collection is said to be infinite, if some of its parts are as big as the whole.
Examples on Infinity
Even though from one point of view the entire list of numbers we count with {1, 2, 3, 4, 5 …}
is twice as large as the list of even numbers {2, 4, 6, 8, 10 …}; the two lists can be matched-up in a
one-to-one fashion.So the two lists are said to be infinite, being exactly the same size.
Even though from one point of view the entire list of numbers we count with {1, 2, 3, 4, 5 …}
is twice as large as the list of even numbers {2, 4, 6, 8, 10 …}; the two lists can be matched-up in a
one-to-one fashion.So the two lists are said to be infinite, being
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