If we nest a natural arithmetic operation we get a new operation. Counting is drawing a number by putting together single quantities. Adding is joining a count with another count or more. Multiplication is adding a number as many times as another number. Exponentiation is multiplying a number as many times as another number. The fith operation, then, is exponentiation of a number as many times as another number. The sixth operation is applying the fith operation to a number as many times as another number. An so on. The nth operation is applying the n-1th operation to a number as many times as another number.
Naming the infinite natural operations. If counting is the first natural operation, adding is the second natural operation, multiplying is the third natural operation, exponentiation is the fourth natural operation, and then there are the sixth natural operation, the seventh natural operation, and so on, the nth natural operation. This way each operation is expressed by an ordinal number and the word operation.
We may think that there is a rule like that a given order natural operation is named by contracting its order number and the word operation in a similar way that addition "add-operation", multiplication "multiply-operation" or exponentiation "exponent-operation" are constructed -I do not mean that this etymology is true, just that it is useful to think that it is.Thus the first operation is firstiation, the second operation is secondiation, the third operation is thirdiation, the fourth operation is fourtiation, the fith operation is fittiation, an so on, the nth operation is ntiation.
Or we may think that we construct a natural operation's name from the expression "applying the nth operation", by omitting the word operation and contracting "applying the nth", like thinking that multiplication comes from "multi-application" thus the first operation is firstplication, the second operation is secondplication, the third operation is thirdplication, the fourth operation is fourthplication, the fith operation is fithplication, an so on, the nth operation is nthplication.
I like more the names firstplication, secondplication, thirdplication, fourthplication, fithplication, an so on, n-thplication.
Naming the infinite natural operations. If counting is the first natural operation, adding is the second natural operation, multiplying is the third natural operation, exponentiation is the fourth natural operation, and then there are the sixth natural operation, the seventh natural operation, and so on, the nth natural operation. This way each operation is expressed by an ordinal number and the word operation.
We may think that there is a rule like that a given order natural operation is named by contracting its order number and the word operation in a similar way that addition "add-operation", multiplication "multiply-operation" or exponentiation "exponent-operation" are constructed -I do not mean that this etymology is true, just that it is useful to think that it is.Thus the first operation is firstiation, the second operation is secondiation, the third operation is thirdiation, the fourth operation is fourtiation, the fith operation is fittiation, an so on, the nth operation is ntiation.
Or we may think that we construct a natural operation's name from the expression "applying the nth operation", by omitting the word operation and contracting "applying the nth", like thinking that multiplication comes from "multi-application" thus the first operation is firstplication, the second operation is secondplication, the third operation is thirdplication, the fourth operation is fourthplication, the fith operation is fithplication, an so on, the nth operation is nthplication.
I like more the names firstplication, secondplication, thirdplication, fourthplication, fithplication, an so on, n-thplication.
Making signs for the infinite operations. Well we have signs: + for addition, * for multiplication, ^ for exponentiation, after these it may used " for fithplication, and it may be used ¨ for sixthplication. We may create more signs like these but it seems that it would be more interesting to have a rule for making signs for natural operations. I think it may be relevant to use a set of number's signs different than the western style numbers, which although we know that come from signs created in India are evolved to somewhat different shapes. I suggest to use the sanscrit's -or the devanagari's- signs for numbers as signs for natural operations. The devanagari's numbers' signs are: ०, १, २, ३, ४, ५, ६, ७, ८, ९. Nevertheless, it may be used as well letters, for example: c, i, n, m, z, a, s, t, x, q as a new sign set for representing 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with the purpose of making signs for the infinite natural operations. (I have suggested these particular letters just because they look to me as having a some relations with the number's signs and at the same time look different enough to not be confused with them.)
Thus, if using the hindi numbers' signs, operations are signed: १ for count, २ for addition, ३ for multiplication, ४ for exponentiation, ५ for fithplication, ६ for sixthplication, ५ for seventhplication, an so on, १० for tenthplication, ११ for eleventhplication, an so on, १०१ for onehundred firstplication, an so on, १०००६९० for onemillion threehundred ninetyethplication and so on, to the nthplication.
And if using the letter as suggested as numbers, then the operation may be signed: i for count, n for addition, m for multiplication, z for exponentiation, a for fithplication, s for sixthplication, t for seventhplication, an so on, ic for tenthplication, ii for eleventhplication, an so on, ici for onehundred firstplication, an so on, icccmqc for onemillion threehundred ninetyethplication and so on, to the nthplication.
For example, using those letters as numbers' signs for making natural operations' signs, we may write:
10+10 which is 10*2 or 10m2
10*10 which is 10^2 or 10z2
10^10 which is 10"2 or 10a2,
10^10^10^10^10^10^10^10^10^10 which is 10"10 which is 10¨2 or 10s2
A rather ridiculous operation:
10+10 which is 10*2 or 10m2
10*10 which is 10^2 or 10z2
10^10 which is 10"2 or 10a2,
10^10^10^10^10^10^10^10^10^10 which is 10"10 which is 10¨2 or 10s2
A rather ridiculous operation:
10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10 which is 10"10"10"10"10"10"10"10"10"10 which is 10¨10 which is 10t2.
So that it is simple to write natural operations with a base number like the base 10. One more example: 10iccccnm8.
So that it is simple to write natural operations with a base number like the base 10. One more example: 10iccccnm8.
