Recent content by Tasaio

Spivak's Calculus, 5(x) -- "Use (ix) backwards..." Homework Statement Prove the following: (x) If a,b\geq0 and a^{2}<b^{2}, then a<b. (Use (ix), backwards.) Homework Equations (ix) If 0 \leq a<b, then a^{2}<b^{2}. The Attempt at a Solution Suppose a,b\geq0 and a^{2}<b^{2}...

Using your coin example, on each toss, there is a 0.5 probability that there is a head. So for 20 tosses, we calculate: 0.5 * 0.5 * 0.5 * ... * 0.5 (20 times) Let's try that for my question. For *each toss*, there is a 30/36 chance that the numbers do not sum to 7. So after 20...

Suppose we make 20 tosses using 2 dice. What is the probability of scoring a two numbers that sum to 7? My attempt The sample space for a single toss of a single die is S = {1, 2, 3, 4, 5, 6} For a single toss of both dice, the sample space is S = {(1, 1), (1, 2), (1, 3), (1, 4), (1...

My textbook uses ( , ) for every event within the sample space -- the sample space itself uses { }. See my original post. My question is, if we have (x, y) and (y, x), where x != y, then should they be considered the same event? We are working with *two* distinct dice. For example, should...

Hi there, This question is giving me some trouble... 1.1-6 A game consists of rolling a pair of dice and moving a game piece the number of spaces according to the total number of dots on the dice. In order to move the game piece on a player's first turn, the player must roll a 1 or a 6...

Hi, Here's my attempt so far... Prove: x^n = y^n and n even --> x = y OR x = -y My attempt Suppose x^n = y^n and n even for n = 1, 2, 3,... Proof by Contradiction: Suppose NOT(x = y OR x = -y) Then x != y and x != -y (by DeMorgan Theorem) Cases: 0 < x < y 0 = x < y x < 0 =...

Hi Byrrg, I'm thinking of game programming as well. At the moment, I'm pursusing a Computer Science specialist in Artificial Intelligence at UofT. I can't give you solid advice, but my advice is to take the CS-designed math courses recommended for the general CS degree. That is, take a...

6. (d) Prove that if x^n = y^n and n is even, then x = y or x = -y My attempt Suppose x^n = y^n and n is even. Then x^n = y^n. And n is even. I'll try Proof by Contradiction. Proof by Contradiction: Suppose !(x = y or x = -y) Then (x !=y and x != -y) by DeMorgan's Theorem ...

Thanks for the replies -- yes I'm talking about the University of Toronto (downtown, the main St. George campus). Also, the professor originally said it was perfectly reasonable to take 5 years for my Computer Science degree, since I was in Life Sciences for the first year However, he...

Yes, I solved it by breaking it into 2 cases: y > 0 and y = 0. :cool:

I'm not in Physics, myself, but I recommend taking the extra fourth year. I don't know about Physics, but for UFT math and CS, the Grad Schools generally only have access to your marks from your *second-last* year -- so if you only take 3 years, they'll be looking at your second year marks...

I'm currently pursuing a BSc at UofT. I've been dying to ask someone's advice about my academic situation -- please tell me what your advice would be. Due to a combination of personal reasons (family pressure, an intimidating teacher who was suspended for punching a student), I completely...

I solved the other 2 cases, but number 2 is giving me trouble. Case: x < 0 \leq y Then x - y < -y \leq 0 Since x < 0 and -y \leq 0 Then x + (-y) \leq x So x-y \leq x Where should I go from here?

6(c) Prove that if x^n = y^n and n is odd, then x = y. Suppose x^n = y^n. Suppose n is odd. Then there exists k in Z, such that n = 2k+ 1. But n >= 1, so k >= 0. We have x^(2k + 1) = y^(2k + 1) We need to prove x = y for all k >= 0. Let's use Proof By Induction. Proof by...

The first result I can think of was: 0 <= x < y --> x^n < y^n, n= 1, 2, 3, ... I can't use this, since the hypothesis has the additional requirement that 0<=x. I'm trying to prove x < y --> x^n < y^n for n odd. (There is no requirement that 0<= x) --- Are you sure that x^n = |x|^n...