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JAIN MATHEMATICS AND KARMAVAD/153
to calculations but it is used for comparison, hence it too, is not endless. Various references where 'infinite' is used are related to the characteristics of six fundamental mattereals, like
• Jiva (bios) consists of infinite pradeshas • Infinite dions (paramanu) combine to form quadons (skandhs) • Group of infinite quadons makes an octon (behavioural paramanu) • Infinite Samay (instant) elapses in an Avalika • Space is comprises of infinite Pradesh.
Besides the eight classifications of 'infinity', words like 'uni-infinity' and 'universal infinity' do appear in the Jain texts. These are used with respect to space and time both. In space, 'uni-infinity' is used for one-dimensional lengths and 'universal infinity' is used for spatial extensions. Similarly, in time, ‘uni-infinity' is used for either the past or the future and 'universal infinity' defines the entire time frame.
We find a specialty in Jain mathematics that the numerate and the innumerate have been placed together. In the Bhagavati-Sutra, a table has been given which formulates the units of time -
Samaya Innumerate samaya
Smallest unit one avalika
Numerate avalika
One breath —
respiration
one respiration
one prana one stoka
Seven pranas
Forty eight minutes
one muhurta etc.
An outstanding fact revealed by this table is that a numerate avalika embrace infinite samay. That is, even infinite could be a part of the finite.
The number scale, as used in Jain texts, starting from numerate and ending at infinitum comprises all the constituents of modern mathematics, highlights of which are -
• Use of arithmetical progression to build the number scale up to 84 lacs. • Use of geometrical progression to continue counting beyond 84 lacs. • Use of statistical quantities like maxima, minima, median and average. • Rejection of absolute zero and absolute infinity.
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