Mathematics

Some dialog: ---------------------------------------------------------------------------------- Doron: I think that we do not understand each other. I gave you MY definiton of the limit concept. Now, please give the standard definition for this concept. After you give the standard definition, then we shall compare between the two approaches. Any way do you agree with http://mathworld.wolfram.com/Limit.html definition? ---------------------------------------------------------------------------------- kaiser: off course I agree with this definition. I meant for you to provide the defintion for the limit of S(n), no need delta epsilon…

Here is another question I posted on PF but got little attention: I need to prove the following identity for Stirling numbers of the first kind: [math]s_{n,2} = (n-1)!\Big(1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n-1}\Big)[/math] For the uninitiated, s[n,k] is a Stirling number of the first kind and represents (as I was explained) the number of ways of sitting n people in k table so that every table has at least one person. The ordering of the tables doesn't matter but the ordering of the people on a table does. Example: Suppose three people (A, B, and C) are sitting at a table such that C is to the right of B and B is to the right of A. So ABC = BCA = C…

Complementary Set Theory Axioms, exmples and explanations can be found in: http://www.geocities.com/complementarytheory/My-first-axioms.pdf I'll be glad to get your remarks and insights, thank you, Doron

The goal of this thread is to find a logical reasoning system, which can be used as a common basis for both our morality development and our technological developments. If we achieve this goal, then I think that we improve our chances to survive the power of our technology. ========================================================================== If we look at Drake's equation http://www.setileague.org/general/drake.htm we can find parameter L. L = The "lifetime" of communicating civilizations, or in other worlds, if there is no natural catastrophe in some given planet, then how some civilization survives the power of its own technology? If we look on…

Hi! i just have a question In class today, we learnt that in a circle, the circumfrence divided by the diameter = Pi, why is this so?

A =1 J=A Z = 1A 8,F,17 1,12,5 18,F,15,12 8,5,19,1,4,5,3,9,D,1,C 13,B,9,C,C,13 .... 9 B,E,F,17 14,8,1,14 18,F,15 C,F,16,5 D,1,14,8 13,F 9 14,8,F,15,7,8 9 17,F,15,C,4 13,8,1,12,5 14,8,9,13 17,9,14,8 18,F,15 !!!!! good luck!

Having trouble with this. Determind whether the following statement is true of false If [math]a_k \in \mathbb{R}[/math] for each [math]k \in \mathbb{N}[/math] and [math]\sum_{k=1}^{\infty}a_k[/math] converges, then so does [math]\sum_{k=1}^{\infty}a_k^2[/math]. If you think the statement is true, prove it. If you think it's false, give an explicit counter-example.

Suppose a, b, and n are positive integers and a + b = n. For what values of a and b maximize ab? The only way I know of maximizing ab is by drawing a table of values and comparing numbers. It seems though that if n = 2k, then the maximum is obtained when a = b = k. If n = 2k + 1, the maximum is obtain when a = k and b = k + 1. Is there an intuitive way of showing/deriving this though. I can't seem to think of anything.

Have your teachers taught you about the mod and absolute value? I want to know whether I will come across with the lessons of these skills. (Actually, I learnt them myself)

Please look at the attached pdf http://www.geocities.com/complementarytheory/Roots-Chain.pdf . By this model we can see that √1 is the "shadow" of √2 and √2 is the "shadow" of √3. I think that we can conclude that √3 is the "shadow" of √4 ... and so on. In short, I am talking about roots which each one of them is the diagonal of its dimension level, where each n_dim diagonal is the "shadow" of n+1_dim diagonal. We have a chain of "shadows" between infinitely many diagonals in |N| dimension levels. Do you think that this "Chain of Shadows" has any mathematical/physical meaning?

[MATH] log(x+y)/logx = log(x+y)/logy[/MATH] Can anybody show a calculation? I think that's a trick.

Today, I read some function book. And I drew a lot of graph, but due to the size and my hand-drawing, the output is very ugly. I want to have a very good graph drawing software. Can you suggest some to me which are free, simple?

Hello everyone, I am going to read some books in my summer holiday. Which region of mathematics involved in science the most? Or which part do you like the most? ( the most or most ???) Would you suggest to me?

I saw a program on tv about a professor that came up with a mathematical equation that says there must be other planets that hold life. I think he worked along with seti,,,but not sure,,,waas wondering if anyone knew what that equation was?

As a new user I haven't been able to see how things have progressed at ScienceForums.net but I believe the users in the Maths forums mostly fall into a few categories: . Varsity Maths Students . Interested High School Students . Interested Members of the general public What I'm concerned about is the possibility of some people who have non-standard/alternative theories that use these forums to debate with those that are still learning what Maths is all about. What do you guys think about adding an extra forum for these alternative theories so that people viewing them know that they are a bit less "mainstream". I think this would ensure that the less "knowle…

I was just curious to know wether the trignometric functions and the log / antilog functions are defined for imaginary and complex numbers....and if yes then how are they defined ?

I have a question, I forget what the symbol is for this set problem: {1,2,3,4,5,6,7,8,9,10} ??? {4,6,8,9,10}= {1,2,3,5,7} What is it???

I have a nice problem for you guys, just a funny problem to stimulate the mind. For each non-negative integer [math]n[/math], let [math]a_n[/math] be the number of digits in the decimal expansion of [math]2^n[/math] that are at least 5. For example [math]a_{16} = 4,since 2^{16}=65536[/math] has four digits that are 5 or higher. What is the sum [math]\sum_{n=0}^\infty \frac{a_n}{2^n}[/math] ? I evaluated machinally the first 299 (see attachment) terms a of the sum. The sum converges to 0.086617 numerically, what is the exact value ? What is the growth rate of a_n ? Mandrake a.txt

check here. http://www-groups.dcs.st-and.ac.uk/%7Ehistory/Day_files/Year.html no one famous was born on my birth day. so sad

Happy pi day everyone...yep its 22/7 meaning its national pi day...so celebrate by using pi

Alpha Day is May 17, the 137th day of the year. The constant alpha is the basic constant in all electro-magnetic interactions and determines among other things why we have the elements we do and what their chemical properties are. So its being the right size and not a few percent different makes life possible. And keeps the sea from blowing up in an H-bomb fusion reaction and makes it so there are stable elements heavier than helium, and so on. It is fundamental to the universe. Alpha reciprocal is about 137.036..., so very close to 137. So a good approximation for alpha is 1/137. Alpha is better than PI

What is the code in mathematica for sigma?

what happened? i thought you were going to put more of your calculus lessons.

[math]x^n+y^n=z^n[/math] This is fermat's enigma, where n>2. However, [math]\sqrt3^4+2^4=\sqrt5^4[/math] is true. Huh???

I am sending my friend an email, but I need to draw up the equation. It is a sigma equation! Anyone know the code for this???