Infinity

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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.

• 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 exactly the same size.

• The distance to the end of a circle is also infinite as there is no such end, which is a continuous loop

• Can you count the sand on the sea beach? You say it is infinite



• Think about the largest natural number? You will always find another number greater to it, and another number
  greater to it, and so on…. So, the list of natural numbers is infinite

What will you get if you divide any number by zero?
Let us try….
= 10, = 100, = 1000, = 10000, … = 1000000, …
You notice that as the denominator reduces, the quotient increases. It can be said
that when the denominator becomes zero, the quotient becomes infinity.So, any number
divided by zero is infinity. The most important thing about infinity is - ? < x < ?,
where x is a real number. So, it can be understood that minus infinity is less than any
real number and infinity is greater than any real number.

John Wallis is actually being credited with introducing ? as a symbol for infinity in 1655. One conjecture
about why he chose this symbol is that he derived it from a Roman numeral for 1000, which was in turn derived from
the Etruscan numeral for 1000,and looked somewhat like CIO and was sometimes used to mean "many".

Another conjecture is that he derived it from the Greek letter ? (omega), the last letter in the Greek alphabet.
Another possibility is that the symbol was chosen because it was easy to rotate the numeral "8" by 90° when typesetting
was done by hand. The symbol is sometimes named as "lazy eight", evoking the image of an "8" lying on its side.
Another popular belief is that the infinity symbol is a clear depiction of the hour glass turned at an angle of 90°
because this action would cause the hour glass to take infinite time to empty, thus presenting a tangible example of infinity.
The invention of the hourglass predates the existence of the infinite symbol thus allowing this theory to be plausible.
The precise origin of the infinity symbol ? is not clear. One possibility can be suggested by the name it is sometimes called — the
lemniscate, from the Latin lemniscus, meaning "ribbon". One can imagine walking forever along a simple loop formed from a ribbon.
A popular explanation is that the infinity symbol is derived from the shape of a Möbius strip. Again, one can imagine walking along its
surface for ever. However, this explanation is not probable, as the symbol had been in use to represent infinity for over two hundred
years before August Ferdinand Möbius and Johann Benedict Listing discovered the Möbius strip in 1858.

There is also a possibility of the inspiration from an old religious / alchemical symbolism. The infinity snake, the
ouroboros symbol (also, uroboros or uroborus) is a serpent or a dragon biting its own tail. The symbols appeared in Egypt
in 1600 BC. It has been associated with the Zodiac on the whole and the eternity of time. It is the symbol of the perpetual
cyclic renewal of life. It has been found in Tibetan rock carvings and elsewhere depicted in the shape of a lemniscate, although
a plain circle is more common because the circle symbolizes infinity in Zen Buddhism. In the Rider-Waite tarot deck, the lemniscate
represents the balance of forces and is often linked with the magician card.

Therefore, the above explanation constitutes the different possibilities / beliefs on how the infinity and its symbol came into existence.
Nevertheless, infinity has great significance in the world of mathematics always!!!

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