Recent content by Hubert

Yes, that's correct.

What have you tried already? If you know the definition of subset, it should be easy enough to make a list of all the subsets and then count them. There is also a very simple formula relating the number of subsets of a given set to its cardinality. After you answer part 1, part 2 is simply...

You have most of the proof down, just a few minor tweaks are needed. Hodge is right that you need to address the limit case as well, but I also think that you mean to construct B_n by adding w_n to B'_n-1 instead of just B_n-1, which isn't clear in your initial examples. It might be easier to...

I think that he is referring to the standard definition of 2 as the set {0,1}.

No there isn't. When Cohen proved the independence of AC he used a model in which there was no well-ordering of the reals.

Or show that 1x2x3x4...is greater than or equal to 2x2x2x2x2... and less than or equal to aleph null^aleph null. Still, this only indicates the factorial is equal to beth_1 without CH, like CRGreathouse said.

Well, if it is a parabola, the equation is of the form y = f(x) = ax^2+bx+c Now, f(-3)=1 and f(0)=0 Finally, f'(0)=0 Also, since f(x)= ax^2+bx+c and f(0)=0 c must also equal zero. I'm not sure how any of this will help you though. EDIT: I think I'm wrong again (as usual). I guess the...

I didn't want to start a new thread, but I have a question of my own: I think essentially what the limit definition says is that \lim_{x\rightarrow a} f(x) = L means for each \epsilon>0 there is a \delta>0 such that f(x) is in the inverval (L-\epsilon, L+\epsilon) whenever x is in the the...

If you start with the standard basics, The sine of an angle is a function which assigns to each angle the ratio of the opposite side to the hypotenuse as if the angle was in a right triangle. The cosine of an angle is is a function which assigns to each angle the ratio of the adjacent side to...

Draw a right triangle. Edit-Nevermind, I misread the question.

No, (1/2)(DC x BE) does not equal the area of triangle BDC. The height must be a line drawn to the vertex of a triangle. EDIT: Nevermind. I just proved that I was wrong.

Since this thread was bumped up recently, just for clarity I meant x^2 + 1=0 . I think that StatusX responded to me as if I said that anyway, but my mistake was bugging me:smile: .

So what is the fault in the "proof"? I assume it has something to do with the fact that both i and 1/i (or -i) are solutions to the equation x^2 -1 = 0, just as both 2 and -2 are solutions to the equation x^2 + 4 = 0.

If you're interested in learning about phi, try picking up Mario Livio's excellent book The Golden Ratio. In it, he describes all of the properties/patterns associated with the number (there are a lot more than those already mentioned) and he also dispels some of those rumors relating to phi's...

But then the smallest such circle would be one in which the longest chord is diameter, andthe radius would be equal to 6.5. I agree, there is not enough information.