Math Is Fun Forum

Thanks alot thats a great help.

There is something in topology called Reimannian manifolds which are manifolds that allow you to measure distances and angles:

http://en.wikipedia.org/wiki/Riemannian_manifolds

or take a look at manifolds in general:

http://en.wikipedia.org/wiki/Manifold

Hi, I've got another question now regarding kurwatowskis theorem. I need to prove:

It seems like it should be so obvious, but I'm having trouble writing a meaningful proof for it, without actually just replacing a with u and b with v.

I'm given the hint that I need to consider the two cases where a=b and

My thoughts are that these cases are:

since a=u and b=v,

I feel like I'm making a mess of it, please help!

Yes I know that, but since {a} is a set and {{a},{a,b}} is a set, and since a is an element of a set, I would have thought I used the relations correctly.

P.S. keep your hair on jane!

The ambiguity was in the fact that although max{} and min{} are self explanatory, the text I was reading kept referencing them to to the formulas Jane provided without explicity stating the equalities, and after finding nothing online I wanted to make sure I wasn't missing something important. You know what they say about asumption being the mother of all **** ups

Hi, you have a function f, taking a single argument, n, and returning a number r, so f(n)=r.

The main problem is the for loop. within the loop you could consider a seperate function:

This reasoning is ok in c, where we write for example r=r+1; to mean take the value stored in the memory location of r, add 1 to it, and save the new value in the original memory location, but writing the equality r=r+1 in mathematics cannot be true for any

.

Also while loops can be used to calculate finite series using

and

and can be readily compared in these cases, something like what you have is not so easy to compare. Usually it's a case of knowing the maths before implementing it as code, rather than trying to extrapolate mathematical expressions from the code.

Hi, I think there is two similar limits that equal e. There is one that is used to describe compound interest:

and there is another one, which I got from this link http://www.mathcentre.ac.uk/students.php/all_subjects/differentiation/first_principles/resources/322 which is:

I don't think you can simply substitute t=0 to get the limit as 1, since the denominator of the exponent becomes zero, so...

...is undefined. If you put in values closer and closer to 0 for x, then you will see the limit gets closer and closer to e.

Ricky, to answer your question, I'm an engineering student, and while I've done calculus and multivariable calculus before, I've forgotten how to differentiate the exponential function from first principles (I never need to do this, it's just a matter of interest), and have never really covered analysis in much depth. I know there are multiple definitions for the exponential function, and I've always considered "the function whose value equals its derivative for all x" to be the 'main' definition, so if you could show me how this limit is equivalent to that or the other limit I gave I would appreciate it.

Also I remember a derivation where the series (Taylor series?) you mentioned can be derived purely from knowing that:

and:

Where somehow my lecturer obtained a series for the function and repeatedly differentiated it. If you know what I'm talking about could you show me that too?

Thanks alot