- Jai Jinendra,An interesting article on Infinity.
**Early Indian views of infinity**

Along with the early conceptions of infinite space proposed by the Taoist philosophers in ancient China, one of the earliest known documented knowledge of infinity was also presented in ancient India in the Yajur Veda (c. 1200–900 BC) which states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

The Indian Jaina mathematical text Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable and infinite. Each of these was further subdivided into three orders:- Enumerable: lowest, intermediate and highest.
- Innumerable: nearly innumerable, truly innumerable and innumerably innumerable.
- Infinite: nearly infinite, truly infinite, infinitely infinite.

The Jains were the first to discard the idea that all infinites were the same or equal. They recognized different types of infinities: infinite in one and two directions (one dimension), infinite in area (two dimensions), infinite everywhere (three dimensions), and infinite perpetually (infinite number of dimensions).

According to Singh (1987), Joseph (2000) and Agrawal (2000), the highest enumerable number N of the Jains corresponds to the modern concept of aleph-null (the cardinal number of the infinite set of integers 1, 2, ...), the smallest cardinal transfinite number. The Jains also defined a whole system of infinite cardinal numbers, of which the highest enumerable number N is the smallest.

In the Jaina work on the theory of sets, two basic types of infinite numbers are distinguished. On both physical and ontological grounds, a distinction was made between asmkhyata and ananata, between rigidly bounded and loosely bounded infinities.

Huston Smith, born in China, a philosopher and religion scholar, has said that in Hinduism: “The invisible excludes nothing, the invisible that excludes nothing is the infinite — the soul of India is the infinite.”

“Philosophers tell us that the Indians were the first ones to conceive of a true infinite from which nothing is excluded. The West shied away from this notion. The West likes form, boundaries that distinguish and demarcate. The trouble is that boundaries also imprison — they restrict and confine.”

“India saw this clearly and turned her face to that which has no boundary or whatever.” “India anchored her soul in the infinite seeing the things of the world as masks of the infinite assumes — there can be no end to these masks, of course. If they express a true infinity.” And It is here that India’s mind boggling variety links up to her infinite soul.”

“India includes so much because her soul being infinite excludes nothing.” It goes without saying that the universe that India saw emerging from the infinite was stupendous.”

Excerpt from : Wikipedia

Regards,Anish Shah - Jai JinendraIt appears the reference to Jain contribution is by my acquaintence Dr Navjyot Singh, I guess.With regardsDev
wrote:*Anish A Shah <anishshah19@...>*ï»¿

Jai Jinendra,An interesting article on Infinity.**Early Indian views of infinity**

Along with the early conceptions of infinite space proposed by the Taoist philosophers in ancient China, one of the earliest known documented knowledge of infinity was also presented in ancient India in the Yajur Veda (c. 1200â900 BC) which states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

The Indian Jaina mathematical text Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable and infinite. Each of these was further subdivided into three orders:- Enumerable: lowest, intermediate and highest.
- Innumerable: nearly innumerable, truly innumerable and innumerably innumerable.
- Infinite: nearly infinite, truly infinite, infinitely infinite.

The Jains were the first to discard the idea that all infinites were the same or equal. They recognized different types of infinities: infinite in one and two directions (one dimension), infinite in area (two dimensions), infinite everywhere (three dimensions), and infinite perpetually (infinite number of dimensions).

According to Singh (1987), Joseph (2000) and Agrawal (2000), the highest enumerable number N of the Jains corresponds to the modern concept of aleph-null (the cardinal number of the infinite set of integers 1, 2, ...), the smallest cardinal transfinite number. The Jains also defined a whole system of infinite cardinal numbers, of which the highest enumerable number N is the smallest.

In the Jaina work on the theory of sets, two basic types of infinite numbers are distinguished. On both physical and ontological grounds, a distinction was made between asmkhyata and ananata, between rigidly bounded and loosely bounded infinities.

Huston Smith, born in China, a philosopher and religion scholar, has said that in Hinduism: âThe invisible excludes nothing, the invisible that excludes nothing is the infinite â the soul of India is the infinite.â

âPhilosophers tell us that the Indians were the first ones to conceive of a true infinite from which nothing is excluded. The West shied away from this notion. The West likes form, boundaries that distinguish and demarcate. The trouble is that boundaries also imprison â they restrict and confine.â

âIndia saw this clearly and turned her face to that which has no boundary or whatever.â âIndia anchored her soul in the infinite seeing the things of the world as masks of the infinite assumes â there can be no end to these masks, of course. If they express a true infinity.â And It is here that Indiaâs mind boggling variety links up to her infinite soul.â

âIndia includes so much because her soul being infinite excludes nothing.â It goes without saying that the universe that India saw emerging from the infinite was stupendous.â

Excerpt from : Wikipedia

Regards,Anish Shah

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