Recent content by B-Con

You still have 5 equations and 5 unknowns. Look at Gauss-Jordan elimination, it's an algorithm that will spit out a solution.

d(y,A) - d(x,A) \geq -d(x,y); Does not imply -d(x,y) \leq -(-d(x,A)+d(y,A)) but the transition between the last two lines of your proof relies on it. You just switched the sides and direction of the inequality (which is fine) and multiplied one side by -1 (not good). If we could do...

That is by definition. The key, I think, is to look at it from the perspective of provability, not the perspective of definition. If a number is not rational we define it to be irrational. But if a number is not provably rational, it may not be provably irrational. The key there being that there...

Thank you. How are you using the term "can" with regards to proving propositions? Do you mean that we have not yet been able to prove such a thing or that it is impossible to prove such a thing with the given set of axioms and system of logic? If you mean "can" in the former sense then I...

I've been researching Constructivism and Godel's Incompleteness theorems as of late. I was hoping to get feedback on this question. In order to do math, we need a set of axioms A and a system of logic L. This pair (A,L) is called "incomplete" if there exist propositions (in the language of A)...

Ah, yes, that's what I was looking for. It slipped my mind. Thanks. So XOR is just addition of vectors over F_2 and satisfies the conditions of a bilinear map.

I think the basic question here is: What is the definition of a linear function in two variables? Ie, if you have +: S×S → S, what must + satisfy to qualify as linear? I can only find examples of linear functions with one variable.

But addition of vectors, by the definition of a vector space, is the dimension-by-dimension addition of the field elements, which uses the field addition. My problem is that, as far as I can find, a linear transformation is from one vector to another vector. XOR is from two vectors to one vector.

In computer science the XOR operation is a very important one, and I've heard XOR referred to as a "linear" function. My experience with linear functions (in the sense of vector spaces) has only been with functions in one variable, but XOR is a function of two. I know that we start by using...

Part B was notably harder than A. I made way too many dumb mistakes. I could've tripled my score if I had just thought more clearly during the test.

We have a homework forum for this. To prove that something does not have discontinuities on a given interval, it suffices to show that all of the function's discontinuities lie outside of the interval. Find the discontinuity(s) for this function then show that they are not in the given interval.

Thanks for the tip, I'll check it out. I figured Gowers was simply someone who I hadn't heard of before. By the way, I like the quote in your sig. Heh, no problem. :-p

Thanks, I got it. Isn't that what a monic polynomial is by definition? Sorry, didn't mean to be ambiguous.

Homework Statement Number Theory homework. I'm supposed to prove that the value 2^.5 + 3^.5 is irrational by finding a monic polynomial that the aforementioned number is a root of. This would be trivial if I were supposed to prove that just 2^.5 was irrational because its monic polynomial...

The first obvious example is base 2, what computers use. Computers really don't have a way of storing "part" of a value, so they deal with litteral "on" and "off" values, which are 1 and 0 respectively. Base 2 is very helpful in this arena because it allows computers to do a lot of math using...