
#37
Sep2311, 10:48 PM

Sci Advisor
HW Helper
Thanks
P: 25,165





#38
Sep2311, 10:53 PM

P: 113





#39
Sep2311, 10:57 PM

Sci Advisor
HW Helper
Thanks
P: 25,165





#40
Sep2311, 11:03 PM

P: 113

does q_i mean "q sub i" if so then, if I have shown that f(q_i)=q_i1.. and since the function is continuous for numbers..then a sequence of rational numbers exists to form an irrational number as the number of terms in the sequence approach infinity?
edit: and this would show that..as i>>infinity...f(q_i)=q_i1...which means the formula is true for the irrational numbers 



#41
Sep2311, 11:10 PM

Sci Advisor
HW Helper
Thanks
P: 25,165





#42
Sep2311, 11:17 PM

P: 113

edit: is it because an irrational number is a sum of decimals? so like pi=3+.1+.04+.001.. 



#43
Sep2311, 11:25 PM

Sci Advisor
HW Helper
Thanks
P: 25,165





#44
Sep2311, 11:27 PM

Sci Advisor
HW Helper
Thanks
P: 25,165





#45
Sep2411, 12:28 AM

HW Helper
Thanks
PF Gold
P: 7,177

And now for extra credit
What happens if you remove the assumption that f(1) = 0? 



#46
Sep2411, 06:28 PM

P: 113

So now can I use induction to prove that the formula is true for all real?




#47
Sep2411, 06:29 PM

P: 113

haha.. does it become an infinite number of functions?...like since a linear function is f(x+y)=f(x)+f(y)...then would removing the assumption give me all linear functions +1? 



#48
Sep2411, 08:38 PM

Sci Advisor
HW Helper
Thanks
P: 25,165





#49
Sep2411, 09:17 PM

P: 113

I show that f(nx)=nf(x)+(n1), where n is an integer. Then, setting x=1 and using the initial condition that f(x)=0, I show that f(n)=n1. Then, setting x=m/n I show that f(m)=nf(m/n)+n1..since f(m)=m1, this becomes m1=nf(m/n)+n1.. so f(m/n)=m/n1 (m and n are integers). Since the function is continuous, it exits for all points and every irrational number has a sequence of rational numbers that approach it and so f(q_i)=q_i1, where q_i is the sequence of rational numbers approaching an irrational number. Since this formula can be derived for all real numbers i can use induction to show that f((n+1)x)=(n+1)f(x)+n equals the original formula 



#50
Sep2411, 09:22 PM

Sci Advisor
HW Helper
Thanks
P: 25,165





#51
Sep2411, 09:32 PM

P: 113

hmm.. Ok I know that since its continuous a point exists everywhere which guarantees the existence of there being a rational number right?..I guess what Im trying to say after that is that since an irrational number is a sequence of rational numbers..then I can take 1 minus those rational numbers. Like pi is (3, .1, .04, .001..) = pi so I can do (31, .11, .41, .0011...) = pi1 by using the formula right?




#52
Sep2411, 09:34 PM

P: 113

maybe if i add like... f(3)+f(.1)+f(.04)+f(.005)....=pi1?




#53
Sep2411, 09:41 PM

Sci Advisor
HW Helper
Thanks
P: 25,165




Register to reply 
Related Discussions  
Double integration of functions involving bessel functions and cosines/sines  Calculus  0  
Spherical Vector Wave Functions and Surface Green's Functions  Advanced Physics Homework  0  
[SOLVED] sum/integral/zeta functions/ Gamma functions  Calculus  3  
Functions and Realtions : Operation on Functions [Please Answer NOW. I need it today]  Precalculus Mathematics Homework  2  
Moment Generating Functions and Probability Density Functions  Set Theory, Logic, Probability, Statistics  4 