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| 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". |
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− | :'''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]] |
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| 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: |
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| 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). |
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− | 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. |
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− | 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. |
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| [[Category: General Reference]] | | [[Category: General Reference]] |
| + | [[Category: Mathematics]] |