That is full, this is full

From the full, the full is subtracted

when the full is taken from the full

the full still remains.”

-Isha Upanishad

The first known use of numbers in India was during the time of the Harappa, about 3000BC. By about 400BC, the Indian Mathematicians were doing extensive work on the idea of infinity. The Surya Prajnapti, a highly revered text in Jainism, defines five kinds of infinity – an infinite line beginning from an endpoint, an infinite line going in both directions, an infinite plane, an infinite universe, and the infinity of time.

In ancient India, acclamations of praise to the air, sky, times of the day or heavenly bodies were expressed in powers of ten that went to a trillion or more. Better known is the story of the young Prince Buddha, who won the hand of Princess Gopa by reciting a number table that included the powers of ten beyond the twentieth decimal place.

The ancient Greeks had immense difficulties with infinity. They could never quite accept as we do today, but did imagine a ‘potential infinity’. Aristotle (384-322 BC) allowed integers to be potentially infinite but not infinite in quantity.

Zeno of Elea (490-430 BC) brought forth several contradictions between the discrete and the infinite. Zeno provided four paradoxes which challenge students of mathematics to this date.

In the latter half of the 19th century, Georg Cantor introduced the infinite into mathematics. In 1874, he published a paper in which he demonstrated the remarkable result that the algebraic numbers can be placed in one-to one correspondence with the natural numbers, while the real numbers cannot. The set of rational numbers is thus shown to have the same size as the set of natural numbers, but the set of real numbers was larger than the set of rational numbers.

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