Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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2.2.2. Madhyama 2.2.3. Utkrsta
2.3. Asamkhyāta
2.3.1. Jaghanya 2.3.2. Madhyama 2.3.3. Utkęsta
3. Ananta (Infinite) 3.1. Parita
3.1.1. Jaghanya 3.1.2. Madhyama
3.1.3. Utkşrţa 3.2. Yukta
3.2.1. Jaghanya 3.2.2. Madhyama 3 2.3. Utkrsta
3.3. Ananta
3.3.1. Jaghanya 3.3.2. Madhyama 3.3.3. Utkrsta
• Two important features of the above classification are (1) the existence of innumerability between the domains of numerability and infinity (2) the existence of infinity greater than another infinity.
Quoting Galileo's work on "continnum of divisibles", as well as on the “Theory of Real Numbers" of Cantor, Bell59 remarks.
“Salv.-I see no other decision that it may admit, but to say, that all Numbers are infinite; Squares are infinite; and that neither is the multitude of squares less than all Numbers, nor this greater than that : and in conclusion, that the Attributes of Equality, Majority, and Minority have no place in Infinities, but only in terminate quantities......” Further, Resolving Simplicius' doubt about the conceit of 'assigning an Infinite bigger than an Infinite' Cantor proceeded to describe any desired number of such bigger Infinities...... For cardinal numbers also cantor described an Infinite bigger than an infinite' to confound the Simpliciuses...... He proved (1874) that the class of all algebraic numbers is denumerable, and gave (1878) a rule for constructing an infinite non-denumerable class of real numbers.
59. Cf. Development of Mathematics, p. 273.
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