Presburger Arithmetic is infinitely axiomatizable. infinitely many axioms included. the statement and it's negation can be deduced from axioms. So it's complete and consistent.
From Godel's Incompleteness theorem. any finite set of axioms cannot be both consistent and complete.
inconsistent...
What is life? If you had not lost your life, when your body go to dust all you have experienced have became eternal and you also have opportunity to experience more.
The question is "What is life?".
if you are something in your brain receiving bio-elertricity, you can ask someone pick you out connect you to a computer and make another world for you.
I agree with you. we don't know future. What we do can change nothing. Everything is in the plan.
We make choices and things happened naturally. Creator supports all things by rules or miracle.
Making choices and things happened depends on grace, so we think that we can do what I want to do...
justifications is a reason for action. If violence comes without a reason which is not violence, maybe violence is justified in order to stop it.
If the reason is violence, maybe all violence is justified or all not.
Otherwise if the problem which causes the violence can be solved...
Homework Statement
From wikipedia Vandermonde matrix is a matrix for all the indices i and j Vij=ai^(j-1).
In Matlab the function A = vander(v) returns the Vandermonde matrix whose columns are
powers of the vector v, that is, A(i,j) = v(i)^(n-j), where n =length(v).
Homework...
A=\left(\begin{array}{cc}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&\frac{1}{2}\\\frac{1}{2}&\frac{1}{2}\end{array}\right)
Find an orthonomal basis for N(A^T)
:smile:
I want to know how to use it in practice.
We can find the coefficients and a function f(x) from x0, x1, ...xn and f(x0), f(x1)...f(xn). These values come from observations. I am sure they are not complex numbers. So, the real trigonometric polynomial is good enough. The question is why we use...