Recent content by duke_nemmerle

Look around here http://www.uccs.edu/~math/vidarchive.html

Ahh, got it |a| = |(a+b)-b| \le |a-b| + |b| which means |a| - |b| \le |a-b| the result immediately follows

I'm looking over a proof and I'm wondering from which principles does it follow that \mid a - b \mid < 1 \to \mid a \mid < \mid b \mid + 1 I can see that |a - b | \le |a| + |-b| = |a| + |b| and that |a| - |b| < |a| + |b| but I just can't connect the dots.

I think I've figured it out by considering a much smaller alphabet and character length. I was obviously overcounting, but now I see that I'm counting the strings with more than one instance of the character several times each.

Homework Statement Given that the ASCII character system has 128 possible characters how many 5 character strings are there with at least one occurence of the '@' symbol. Homework Equations The Attempt at a Solution So clearly which symbol we're using doesn't matter, and I see...

I think the real trick on this was to use strong induction and notice that P(n+1) is implied by assuming P(1)...P(n) are true. Specifically, if P(n-2) is true, then P(n+1) is implied because it is three more than it, so if P(n-2) were written as 5a+3b, P(n+1) is 5a + 3(b+1)

Homework Statement Show, by induction, that for all whole number of Roubles greater than 7, the amount can be given without change by using only 3 rouble and 5 rouble notes.Homework Equations In other words for all n \in N, n > 7, there exist a, b \in N such that n = 5a + 3b The Attempt at a...

Ahh, I bet that will do it for me. I had never gotten it completely factored until now, and even if I had I may not have noticed it. I'm going to walk down the hall real quick and I'm sure I'll figure out how the product of three consecutive integers should be a multiple of both 2 and 3, ie of...

Homework Statement Show that if n = m^3 - m for some integer m, then n is a multiple of 6.Homework Equations The relevant information is we don't know modular arithmetic yet, and the only methods of proof we have available are direct proof, contradiction, and counterexample.The Attempt at a...

Hopefully you'll realize that there's NOTHING you can do to get out from under college loans, short of dying or sneaking out of the country. They will take your income taxes without taking you to court, take your social security, whatever they have to do. Spend some time at...

I'm a math major who is about to have his first brush with transition to upper math courses this coming fall. I took the calculus sequence at a local community college, and when I'm looking at some of the problems here or looking at syllabi of courses I will be taking someday, I get the...

be sure to click through the uccs link in the math section, many undergrad courses in there that I've yet to see anywhere else as video lectures

Yeah, I had actually found the force using an equation that is only good for static fluids, I'm going to see if using Bernoulli gets me the same result both ways. Thanks :)

Homework Statement Water is pumped steadily out of a flooded basement at a speed of 5.0 m/s through a uniform hose of radius 1.0 cm. The hose passes out through a window 3.0m above the waterline. What is the power of the pump? Homework Equations The Attempt at a Solution I...

I was in a similar situation and I just went for it. Luckily I could afford to be out of the workplace for a while. I'm doing math right now, and like someone else said, it's almost all about hard work. If you put in 60+ hours a week, you'll find yourself doing stuff you never thought you...