**Bellafiore:** I have a question Let f_n be a sequence of functions defined on a set S. Prove that f_n converges uniforly to f on S iff lim n — infinity {sup {fx – f_nx s.t x E } = 0

**Blaydes:** Use the definition of limit

**Koes:** And compare with the definition of uniform convergence

**Dyches:** That should follow pretty directly from the definition

**Garski:** Ye ur right the is direct

**Whittum:** Ohhh oke I got the — by permilnearly test

**Veth:** I got it directly by definition

**Mischnick:** Im not sure how to apply the definition of linear transformations Tu + v = Tu + Tv in the case of Tx_1, x_2, x_3 = -4x_2, 7x_3, can anyone help me understand?

**Talas:** B0g: in that case, x_1, x_2, x_3 + y_1, y_2, y_3 = x_1+y_1, x_2+y_2, x_3+y_3, and similarly for x_1,x_2 + y_1,y_2.

**Tobola:** And rx_1, x_2, x_3 = r x_1, r x_2, r x_3.

**Mischnick:** Penez: so this transformation isn’t linear?

**Fiwck:** B0g: no, it is linear.

**Mischnick:** I don’t understand this at all :

**Hodge:** If u in C{2}A cap Cbar{A} can I conclude that it derivative belongs to L2A ?

**Blend:** B0g: for example, Tu+v = Tx1+y1, x2+y2, x3+y3 = -4×2+y2, 7×3+y3 = -4×2, 7×3 + -4y2, 7y3 = Tx1,x2,x3 + Ty1,y2,y3

**Mischnick:** Penez: i guess i don’t understand how you can go from Tu+v to -4×2, 7×3 + -4y2, 7y3 and back to Tu + Tv in that example

**Osterdyk:** B0g: you don’t understand how to go from -4×2+y2, 7×3+y3 to -4×2, 7×3 + -4y2, 7y3?

**Mischnick:** Penez: is this similar to a function of x, Fx = x2, where you can input, say, x + y, and in this case end up with x + y2?

**Jarmin:** B0g: the only similarity to that is that a function is involved.

**Kastendieck:** Are you aware that “transformation” means Doody the same thing as “function”?

**Schwiebert:** Okay, well there you go.

**Mischnick:** Can i consider it a “vector function”?

**Mischnick:** I see i see. interesting

**Auck:** In your case, it’s a function from vectors with 3 components to vectors with 3 components.

**Mcluen:** A function from R3 to R2, perhaps, or maybe from C3 to C2.

**Pyfrom:** Http://puu.sh/cmOns/6b6d6719f0.png

**Pyfrom:** Can Panos find where i misstepped?

**Pyfrom:** It’s 2nd order differential equations with undetermined coefficients

**Mischnick:** Penez: that part i somewhat understand. thank you for your help

**Mischnick:** This cl*** is somewhat frustating. all of the homework is online and i feel like im not learning how to do the proofs properly with 100% multiple choice answers for “proofs”

**Ballina:** Let’s see some ID math553

**Syner:** How I can put 5/3 ub atex=

**Drozda:** Pyfrom: the background colours of those fields suggest that your mistake was in solving for c_1 and c_2 given those initial conditions.

**Gallager:** How I can put 5/3 in latex?

**Arnoux:** And indeed I solved them myself and obtained different solutions.

**Bandura:** Or tfrac53, if you want it to fit nicely in a line.

**Pyfrom:** Yes, i probably messed those up, i wasn’t sure whether to include y_p in the solving for c_1 and c_2

**Bantug:** Hi, is Panos familiar with polynomial chaos?

**Girouard:** Of course you do include y_p, since the initial conditions are explicitly written in terms of y = y_p + y_c.

**Lavergne:** Is anyone familiar with the feynman propagator, by chance?

**Goffredo:** I want a horizontal fraction

**Pyfrom:** And i row reducerow reduce

**Ramsdell:** Does anyone know a bigger chat services for math?

**Mischnick:** Penez: would this just have a 1×3 A matrix then?

**Mulryan:** Pyfrom: your row reduction was incorrect, then.

**Solonika:** But the system is correct.

**Levites:** I would like to prove that the set M of all ordinals corresponding to a countable set is itself uncountable. Here is what I am trying . let s be the ordinality of M, then we can consider M as containing the ordinals {1, ., s-1}.