The *asaṃkhyāta *(innumerable) is classified into three types:

1. *Parīta Asaṃkhyāta *(P. A.)

2. *Yukta Asaṃkhyāta *(Y. A.)

3. *Asaṃkhyāta Asaṃkhyāta *(A. A)

Each of the above is again of three types:

1. *Jaghanya *(Minimum)

2. *Madhyama *(Middle)

3. *Utkṛṣṭa *(Maximum)

In this way, there are nine types of *asaṃkhyāta*. Let us consider each of them one by one.

**1.**

*Jaghanya Parīta Asaṃkhyāta*(J. P. A.)By adding one to U. S. we get the value of *Jaghanya Parīta Asaṃkhyāta *(J. P. A.).

Thus

J. P. A. = (U. S.) +1

**2.**

*Madhyama Parīta Asaṃkhyāta*(M. P. A.)The numbers from [(J. P. A.)+1] to [(U. P. A.)-1] are called M. P. A., thus

[(J. P. A.)+1] ≤ M. P. A ≤ [(U. P. A.)-1]

**3.**

*Utkṛṣṭa Parīta Asaṃkhyāta*(U. P. A.)[(J. Y. A.)-1] is called U. P. A.

U. P. A. = [(J. Y. A.)-1]

**4.**

*Jaghanya Yukta Asaṃkhyāta*(J. Y. A.)J. P. A. raised to itself^{[1]} is called J. Y. A.

J. Y. A. = (J. P. A.)

**5.**

*Madhyama Yukta Asaṃkhyāta*(M. Y. A.)The numbers from [(J. Y. A.)+1] to [(U. Y. A.)-1] are called M. Y. A, thus

[(J. Y. A.)+1] ≤ M. Y. A. ≤ [(U. Y. A.)-1]

**6.**

*Utkṛṣṭa Yukta Asaṃkhyāta*(U. Y. A.)[(J. A. A.)-1] is called U. Y. A.

U. Y. A. = [(J. A. A.)-1]

**7.**

*Jaghanya Asakhyāta Asaṃkhyāta*(J. A. A.)There are two definitions.

(I) By raising J. Y. A. to itself^{[2]} we get the value of J. A. A.

(J. A. A) = (J. Y. A)(J. Y. A)

(II) By squaring^{[3]} J. Y. A., we get J. A. A.

It means,

J. A. A. = (J. Y. A)^{2}

**8.**

*Madhyama Asaṃkhyāta Asaṃkhyāta*(M. A. A.)The numbers from [(J. A. A.)+1] to [(U. A. A.)-1] are called M. A. A.. It means,

[(J. A. A.)+1] ≤ M. A. A. ≤ [(U. A. A.)-1]

**9.**

*Utkṛṣṭa Asaṃkhyāta Asaṃkhyāta*(U. A. A.)We get four definitions of *Maximum Asaṃkhyāta Asaṃkhyāta*:

I. By raising J. A. A. to itself and subtracting one from it^{[4]} gives U. A. A. It means

U. A. A. = {(J. A. A)(J. A. A)-1}

II. Firstly, the square of J. A. A. is squared. Then, the following sets of *asaṃkhyāta *magnitude^{[5]} are added in the above result. Then again obtained magnitude is squared three times. Then one is subtracted from the result. What we obtain is the magnitude of U. A. A.^{[6]} The sets added are^{[7]}:

(1) The total number of *ākāśa-pradeśas *(space-units) of the *loka*.^{[8]}

(2) The total number of *pradeśas *of the *dharmāstikāya*.^{[9]}

(3) The total number of *pradeśas *of the *adharmāstikāya*.^{[10]}

(4) The number of *pradeśas *of a single *jīva *(soul).^{[11]}

(5) The *adhyavasāya-sthānas*^{[12]}(the number of states of subtlemost consciousness) which are the cause of the *sthiti-bandha *(bondage qu duration of *karma*).

(6) The *adhyavasāya-sthānas*^{[13]} which are the cause of the *anubhāgabandha *(bondage qu intensity of *karma*).

(7) the indivisible units of the mental, vocal and bodily activities (*yoga*).^{[14]}

(8) The total number of *samayas *of one *kālacakra *(timecycle).^{[15]}

(9) The total number of *pratyekaśarīrī jīvas *(the souls whichare possessed of individual body).^{[16]}

(10) The total number of the bodies of the *anantakāyika *(*nigoda*) *jīvas *(the souls which are possessed of common body).^{[17]}

Thus, if the total number of all the above ten sets is p, then

U. A. A. = {(J. A. A)8+(p)8}-1

III. The third definition of U. A. A. is as follows:^{[18]}

Firstly, the number J. A. A. is made to undergo three times the operation called *vargita-saṃvargita *(in short, V.-S.).^{[19]} Then the following six sets are added to the result:

(1) The total number of *pradeśas *of the *dharmāstikāya*.

(2) The total number of *pradeśas *of the *adharmāstikāya*.

(3) The total number of *pradeśas *of the *loka-ākāśa *(cosmic space).

(4) The total number of *pradeśas *of one *jīva *(soul).

(5) The number of *pratyeka vanaspati jīvas *which are *pratiṣṭhita*.^{[20]}

(6) The number of *pratyeka vanaspati jīvas *which are *apratiṣṭhita*.^{[21]}

Now, the magnitude which is thus obtained is again made to undergo three times the operation of V.-S. and the following four sets of *asaṃkhyāta *magnitude are added:

(1) The total numebr of *samayas *of one *kalpakāla *(one *utsarpiṇī *and one *avasarpiṇī*).

(2) The *adhyavasāya-sthānas *which are the cause of the *anubhāgabandha *(bondage qu intensity of *karma*).

(3) the indivisible units of the mental, vocal and bodily activities (*yoga*).

(4) The total number of *samayas *of one *kālacakra *(timecycle).

Now, the magnitude which is thus obtained is again made to undergo three times the operation of V.-S. Now, one is subtracted from the magnitude thus obtained. The result thus obtained is

U. A. A..

Thus, if J denotes the *Jaghanya Asaṃkhyāta Asaṃkhyāta*, then by thrice operating V.-S., we get

Now, if the magnitude added first is m_{1}, then we get

If we call this magnitude j′ then operating thrice V.-S., we get

Now, if we add the magnitude m_{2}, we get

If we call this magnitude j′′ then

IV. The fourth definition of U. A. A is as follows:^{[22]}

Firstly, make J. A. A. undergo the operation V.-S. J. A. A. times. The magnitude thus obtained is again made to undergo the same operation that many times. the magnitude thus obtained is again made to undergo the same operation that many times.^{[23]}Now, the aforementioned six sets of *asaṃkhyāta *magnitude (see. pp. 377--378) are to be added to the result obtained. Again, the obtained magnitude is made to undergo the operation '*śalakātrayaniṣṭhāpana*'. Now, the aforementioned four sets of *asaṃkhyāta *magnitude (see. p. 378) are added to the magnitude thus obtained. Again the obtained magnitude is made to undergo operation '*śalakātrayaniṣṭhāpana*'. Now by subtracting one from the magnitude thus obtained we get what is called U. A. A..

*yāvat pramaṇao yo rāśirbhavet svarūp asaṃkhyayā. sannyasya tāvato vārān, guṇito'bhyāsa ucyate.. - Lokaprakāśa*, 1.165

*Jaghanyayuktā saṃkhyātaṃ prāgvadabhyāsatāṃitam.*

*hīnamekena rūpeṇa yuktāsaṃkhyātakaṃ guru..*

*etadeva rūpayuktasaṃkhyāsaṃkhyakaṃ laghu. - Lokaprakāśa*, 1.173-174

*jahaṇṇaeṇaṃ juttāsaṃkhejjaeṇaṃ āvaliyā guṇiyā aṇṇamaṇṇabbhāso*

*paḍipuṇṇo jahaṇṇayaṃ asaṃkhejjāsaṃkhejjayaṃ hoi. Aṇuogadārāiṃ*, *Sūtra *593.

*jaṃ taṃ jahaṇṇaṃjuttāsaṃkhejjayaṃ taṃ sayaṃ vaggido ukkasajuttāsa*

*ṃkhejjayaṃ adicchidūṇa jahaṇṇamasaṃkhajjāsaṃkhejjayaṃ gaṃtūṇaṃ paḍidaṃ. - Tiloyapaṇṇattī*, 4.310

*jaghanyayukāsaṃkhyātaṃ vargitaṃ rūpavarjitam.*

*Utkṛṣṭaayuktāsaṃkhyātaṃ prāptarūpaiḥ prarūpitam..*

*ekarūpeṇā yuktaṃ tadasaṃkhyāsaṃkhyakaṃ laghu.*

(This is the opinion of *Karmagrantha*). -* Lokaprakāśa*, 1.186-187

*jhaghanyaāsaṃkhyāsaṃkhyātaṃ bhavedabhyāsatāḍitam.*

*ekarūponitaṃ jyeṣṭhāsaṃkhyāsaṃkhyātakaṃ sphuṭam..- Lokaprakāśa*, 1.175

*jahaṇṇam asaṃkhajjāsaṃkhejjayaṃ jahaṇṇaya asaṃkhejjāsaṃkhejjyamettā*

*ṇaṃ rāsīṇaṃ aṇṇamaṇṇabbhāso ruvūṇo ukkosayaṃ asaṃkhejjāsaṃkhejjayaṃ hoi. - Aṇuogadārāiṃ*, *Sūtra *595.

We do not exactly know to which kind these sets of *asaṃkhyāta *belong, but probably they belong to *Madhyama Asaṃkhyāta Asaṃkhyāta*

*Lokaprakāśa*, 1.188-196

his definition is as per the version of *Karmagrantha*. Also, see *Anuyogadvāra Sūtra *ed. by Ātmārāmji Mahārāja, Uttarārddha, p. 243 footnote

The definitions of these sets of *asaṃkhyāta *magnitude are given in the technical terminology of the Jain philosophy; one has to refer to treatises of Jain philosophy to understand their exact meaning. (Cf. *Technical Terms of Jain Philosophy *by Ācārya Mahāpraja).

The total number of *pradeśas *of each *dharmāstikāya*, *adharmāstikāya*, *lokaākāśa *and a single *jīva *(soul) are the same. *Jain-Siddhānta-Dipikā*, 1.25.

"*asaṃkhyayāḥ pradeśāḥ dharmādharmalokākāśaikajīvānām.*"

The association of the *karma-pudgalas *with soul is called '*bandha*' (bondage). The determination of the duration of such bondage is called *sthitibandha *and that of the intensity of such bondage is called *anubhāgabandha*. There are *asaṃkhyāta *(innumerable) intermediate states of duration and intensiy of karma between the maximum and minimum duration and intensity of karma respectively. The cause of these states are basically the *adhyavasāyas *(subtlemost states of consciousness (soul)) which are also *asaṃkhyāta *(innumerable). They are innumerable times the number of *pradeśas *of the *lokākāśa *(cosmic space).

*Yoga *(activities) of mind, speech and body are undertaken with the *vīrya *(energy) of soul. The number of *prativiṣiṣṭa *(maximum) number of indivisible units of the *vīrya *imagined by an omniscient is also *asaṃkhyāta *(innumerable).

1 *kālacakra *= 20x10^{7}x10^{7} *sāgaropamas*. See Appendix II (supra pp. 350-353) for the total number of *samayas *in 1 *sāgaropama*.

There are two types of mundane souls:

(i) *Pratyekaśarīrī Jīva *: The *jīva *(soul) which is possessed of its own individual body is called *Pratyekaśarīrī Jīva*. The total number of such souls is *asaṃkhyāta *(innumerable).

(ii) *Anantakāyika (Nigoda) Jīva *: When infinite number of souls occupy a single body (which is common to all), they are called *anatakāyika jīvas *or *nigoda*. The number of such bodies is also *asaṃkhyāta *innumerable).

*vargitasaṃvargita*(V.-S.) is that it is raised to power itself once. Thus, if k is made to undergo this operation once, the result will be k

^{k}. The meaning of twice making a number undergo the operation of

*vargitasaṃvargita*(V.-S.) is that once it is made to undergo the above operation and whatever magnitude is obtained is again made to undergo the same operation. Thus, by making k undergo this operation twice, the result would be {{5b841cf69d85e1bf3549d5b97ac5f98d0791621f}} By making k undergo this operation three times, the result would be {{4756713f75ea9b5bc86bc0fb028cb769011db5a8}}