08/22/2012, 02:05 PM
one of the main applications of numbers is being able to solve polynomial equations where the coefficients are those numbers.
since all multiplications and additions are defined we could try to solve 2nd and 3rd degree polynomials.
but a polynomial equation of degree n can have more than n solutions for non-complex numbers. although max n for real numbers.
also we use properties like unique factorization , distributivity etc for solving polynomials in C.
the situation here is different.
2 questions come up naturally.
1) what properties do we have and lack with these +,-,ยง numbers ?
2) how many distinct solutions does an equation of degree n maximally have in function of n ?
this is just for self-consistancy and basics , questions like usefullness and such are of course not yet considered.
it is intresting to note that degree 1 equations can have 2 solutions.
im guessing that an equation of degree n has at most 2n distinct solutions but thats a wild quick guess.
regards
tommy1729
since all multiplications and additions are defined we could try to solve 2nd and 3rd degree polynomials.
but a polynomial equation of degree n can have more than n solutions for non-complex numbers. although max n for real numbers.
also we use properties like unique factorization , distributivity etc for solving polynomials in C.
the situation here is different.
2 questions come up naturally.
1) what properties do we have and lack with these +,-,ยง numbers ?
2) how many distinct solutions does an equation of degree n maximally have in function of n ?
this is just for self-consistancy and basics , questions like usefullness and such are of course not yet considered.
it is intresting to note that degree 1 equations can have 2 solutions.
im guessing that an equation of degree n has at most 2n distinct solutions but thats a wild quick guess.
regards
tommy1729