Changes

The [[Isha Upanishad]] of the [[Yajurveda]] (c. 4th to 3rd century BC) states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

The [[Isha Upanishad]] of the [[Yajurveda]] (c. 4th to 3rd century BC) states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

:'''Pūrṇam adaḥ pūrṇam idam}}''' (That is full, this is full)

:'''Pūrṇam adaḥ pūrṇam idam''' (That is full, this is full)

:'''pūrṇāt pūrṇam udacyate}}''' (From the full, the full is subtracted)

:'''pūrṇāt pūrṇam udacyate''' (From the full, the full is subtracted)

:'''pūrṇasya pūrṇam ādāya}}''' (When the full is taken from the full)

:'''pūrṇasya pūrṇam ādāya''' (When the full is taken from the full)

:'''pūrṇam evāvasiṣyate'''}} (The full still will remain.) - [[Isha Upanishad]]

:'''pūrṇam evāvasiṣyate''' (The full still will remain.) - [[Isha Upanishad]]

The Indian [[Indian mathematics|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:

The Indian [[Indian mathematics|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:

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

The [[Jainism|Jains]] were the first to discard the idea that all infinites were the same or equal. They recognized different types of infinities: infinite in length (one [[dimension]]), infinite in area (two dimensions), infinite in volume (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 number|aleph-null]] <math>\aleph_0</math> (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.

According to Singh (1987), Joseph (2000) and Agrawal (2000), the highest enumerable number ''N'' of the Jains corresponds to the modern concept of [[Aleph number|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 [[Set theory|theory of sets]], two basic types of infinite numbers are distinguished. On both physical and [[Ontology|ontological]] grounds, a distinction was made between {{IAST|''asaṃkhyāta''}} ("countless, innumerable") and ''ananta'' ("endless, unlimited"), between rigidly bounded and loosely bounded infinities.

In the Jaina work on the [[Set theory|theory of sets]], two basic types of infinite numbers are distinguished. On both physical and [[Ontology|ontological]] grounds, a distinction was made between ''asaṃkhyāta'' ("countless, innumerable") and ''ananta'' ("endless, unlimited"), between rigidly bounded and loosely bounded infinities.

[[Category: General Reference]]

[[Category: General Reference]]