Advanced Search
All Posts : Education

I just feel that if at least one person less experienced than me reads this it will be a worth while post, because it will help them avoid things that eluded me when I was younger.


 

The omitted function definitions are not relevant to the reason for which I decided to post about this. I would like the maple user to simply observe how many variables are involved in the relation's (R) three equalities in the consideration of the output.

 

The reason I believe this is important, is that it is sometimes very easy to believe induction is sufficient proof of the truth value of a relation over the superset of a subset that has been enumerated, much like the example of the coefficients of the
"105^(th) cyclotomic polynomial if one were to inductively reason statements about the coeffiecents of the previous 104 polynomials."

 

 

A[n, k, M] = abs(C[0](n, k, M))/abs(C[1](n, k, M)); B[n, k, M] = abs(C[0](n, k, M))/abs(C[2](n, k, M)); E[n, k, M] = abs(C[1](n, k, M))/abs(C[2](n, k, M))

R

"`𝓃`(A[n,k,M])=`𝓃`(B[n,k,M]), `𝓃`(E[n,k,M])=`𝒹`(A[n,k,M]),`𝒹`(B[n,k,M])=`𝒹`(E[n,k,M])]"

> 

for t to 7 do R(t, 2, 30) end do

[1 = 1, 1 = 1, 1 = 1]

  

[1 = 1, 1 = 1, 1 = 1]

  

[1 = 1, 1 = 1, 1 = 1]

  

[1 = 1, 1 = 1, 1 = 1]

  

[1 = 1, 1 = 1, 1 = 1]

  

[1 = 1, 1 = 1, 1 = 1]

  

[1 = 11^(1/2)*7^(1/2), 11^(1/2)*7^(1/2) = 1, 7 = 7]

 (1)


 

Download INDUCTION_IS_NOT_YOUR_FREN.mw
induction

Please Wait...