Recent content by Korisnik

Is it guaranteed that when I have any kind of function ##f##, that I'll be able to find constants ##c## and ##n_0## if I know ##g## by simply adding up the factors multiplying all the terms in the equation? Suppose ##f(n) = a\cdot n^{143} + b \cdot n! + d \cdot (n!)! + m \cdot 2^n - p \cdot...

Thank you for your reply. Do you see the example the professor shows next, where there's a very simple one-row "game space" (this blue environment Pacman moves in) of only a few possible spaces, with a dot in each corner, left and right. So, this is a different scenario where at the beginning...

Hello! I've been following Berkeley's AI course, and I'm a little stuck. In this video , at 1 hour, 11 minutes, and 55 seconds, there's a short simulation of what they claim to be a depth-2 minimax algorithm applied to the Pac-Man scenario with two dots. Pac-Man begins in the corner. The...

...which I could've gotten without the equations obtained by the author of the book. So what is their purpose? I'm not practicing (dis)proving the injectivity, but the logic of proving "obvious" statements formally.

The explanation the book provides is: "The solution of the equation is ##|a| = |b|##, that is, we have 4 solutions in ##\mathbb{R}##, which means that the given implication does not hold because ##a## and ##b## obviously don't have to be equal; consequently, the proposition is false." I'm...

Thank you. Would you mind addressing my question? So far I've found one "explanation", where the author says that "it is obvious", after finding the solutions to the equation.

Homework Statement Prove that ##f: \mathbb{R}\to\mathbb{R}, f(x) = x^2## is not injective. Homework Equations Definition of an injection: function ##f:A\to B## is an injection if and only if ##\forall a,b \in A, f(a) = f(b) \Rightarrow a = b##. The Attempt at a Solution ##f...

Hmm, I think I see what you're trying to say: let ##h_i## be height of body ##i## as a function of time, and ##\Delta h## a constant: then ##h_b=h_c+\Delta h##. Differentiating the equation $$\begin{align}\frac{\mathrm d{h_b}}{\mathrm d{t}}&=\frac{\mathrm d}{\mathrm d{t}}(h_c+\Delta h)\\...

Homework Statement The chain comprising three rings (each of mass ##0.25kg##) is suspended from a massless rope, and a pulling force ##\left(F=9N\right)## is exerted upwards on the rope. Picture: http://i.imgur.com/xeaiBsc.jpg?1. I need to find the values of all the unknowns. Homework...

Okay, I guess you're right. I should leave it alone.

Homework Statement Show that every partition of X naturally determines an equivalence relation whose equivalence classes match the subsets from the partition. Homework Equations ( 1 ) we know that equivalence sets on X can either be disjoint or equal The Attempt at a Solution Let Ai be a...

Right, I get sqrt(2)*2t + 2t^2 + 1 = m, m is integer. Can't be. Thanks. :)

2k = 4t^2, t \in Z, so k is even. 2k = 4t^2 + 4t + 1, so now 2 times k is an odd number, which it can't be, as k is integer: 2k = 2(2t^2 + 2t) + 1 = 2m + 1 (t and m aren't specified, but are integers). And we know that odd squared gives odd, and even squared gives even, not odd, so k can't be...

Thanks for catching that. I'm not sure what you mean by that, as decimal numbers (possibly square root of 2k) don't have parity. The obvious is that the sign changes depending on k.

Alright, so ##T = \sqrt{k\pi}, k\in\mathbb{Z}##, as ##T>0##. Now ##x = \sqrt{\frac{\pi}{2}}## so ##f\left(\sqrt{\frac{\pi}{2}}\right) = 1## and ##f\left(\sqrt{\frac{\pi}{2}} + \sqrt{k\pi}\right) = \sin\left(\frac{\pi}{2} + k\pi +2\pi\sqrt{\frac{k}{2}}\right)## which will equal ##1## iff...