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Unary numeral system is simplest numeral system. following numbers are base 10 and base 1 numbers. 3=111 18=1111....(18 times 1) 1000=111....(1000 times 1) we can write 10, 100, 1000, without zero. here we use only number 1. zero is used only for additive identity.

Unary - Addition 111+11=11111 In base 10 - place 1, place 2,place 3 are 1, 10, 100 respectively. In base 1 - place 1, place 2, place 3, are 1, 1, 1 respectively. we can not write down onecimal (like decimal) here. only we can write fraction form here. 1/5=1/11111

unary subtraction 11111-11=111 easy method is calculation by base 10. 5-2=3 we can directly use base 10 in unary number system. 111....(100 times 1)-111...(20 times 1)=111...(80 times 1)

unary multiplication 111*11 =111+111 =111111 unary multiplication is a simplest multiplication. every thing multiply by 1 111....(150 times 1)*111....(10 times 1)=111....(1500 times 1) In unary, we can multiply by base 10 and we can write by base 1. In unary, we use only number 1

Unary Division 1111/11=11 use base 10 in unary division. 1111....(80 times 1)/111...(20 times 1)=1111 11111/11=11+1/11 Only we should write fraction form in unary. We can not write point form(like decimal point) in unary.

Unary Exponential 111^11 =111*111 =111+111+111 =111111111 it is simplest method. only we want to know multiplication of one. we use only number 1.

Unary Exponential- big number 1111....(100 times 1)^11 111...(100 times 1)*111...(100 times 1) Multiply by base 10 then Write by base 1 11111....(10000 times 1) It is easy method. Only we use number 1.

Unary - proper fraction 11/111+111/1111 L.C.M=111*1111=111....(12 times 1) 11*1111/111....(12 times 1) +111*111/111...(12 times 1) 111...(17 times 1)/111...(12 times 1) 1+11111/111...(12 times 1) we can calculate all the calculation in base 10. we can write by base 1.

From comparison test 1/1+1/2+1/3+1/4+1/5+... > 1+1/2+ (1/4+1/4) +... We take supremum ½ in this series. > 1+1/2+1/2+1/2+... +1/2+.. >1+n/2+infimum , here n=supremum When series passed the supremum elements, series of elements reached the infimum . Limit of infimum=0 >1+n/2

Series of reciprocal of even numbers. 1/2+1/4+1/6+... If the denominators are increased, value of elements are decreased. when the term of series reached the supremum, the value of series reached the infimum. Limit of infimum=0 Therefore, series is convergence.

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead - By ARISTOTLE. My principle states that In a race, quickest runner must overtake the slowest.