Mathematics

whats everyones mathematics skills? And what areas of maths do you reckon have helped you the most?

I put this challenging puzzle in the “Brain Teaser and Puzzles” forum but nobody tried to solve it so far, so I decided to post it in this forum as well. I hope it does not amount to a “spam”.

OK I admit I thought I was losing my sanity when I thought of this, but then I realized people thought Galileo was crazy when he said that the Earth went around the Sun. I am a (fairly)good mathematician and I know better than to question integer division by zero is undefined, but what about 0/0. Basically, for the past one week I was thinking about 0/0. Not integer division by zero but only about zero divided by zero. To prevent "You must be out of your mind" replies, I would like to state the.... uh.... rules first. Here's my theory. f(x) = x/x is a constant function giving the value 1. Therefore, 0/0 is also 1. IF you're going "OMG, Gasp.... what a sacrilege…

I am a layman trying to understand above theorems. This could be a stupid question. Does these theorems imply that we actually cannot prove that 2+2 = 4??? Is this one of the implications of these theorems???

Here is an inline synopsis without using latex. and with lots of deletions to save space. the original is post 13 in the thread on manual evaluaiton of exponents. johnny asked me to point out where I thought it was wrong so here it is. no, you are presuming that 0! is writable as a product (it is - the empty product, but I suspect you don't get that) you have rewritten the taylor series and introduced a mistake. The next bit is you attempting to correct this self introduced mistake. yes, why tell us? note this product is indexed from 1 to 0. This isn't allowed. no, it was caused by you thinking 0! was a product from 0 to 1. at be…

The title is self explanatory. I would like to hear different people's answer to this.

I'm amazed by how many people fail to accept repeated proofs of .999... = 1 utilizing multiple methodologies. Don't read the body of this blog, just read the comments: http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html There are some rather intelligent people making revprez-style bombasitc arguments towards the contrary. Why? What fundamental misunderstanding compels these people?

What is the minimum number of properties posessed by members of a set?

Here is proof that a+bi=-a+bi: Using the distributive proprty, we can write a+bi as i(a/i+b). a/i is also equal to ai, so then it becomes i(ai+b). That equals ai2+bi, and i2=-1, so therefore it makes -a+bi. Equation form of proof: a+bi=i(a/i+b)=i(ai+b)=ai2+bi=-a+bi Proof that a/i=ai: Because i2=-1, we can write a/i as a/-11/2. a is also sq.root(a2), or a2/2, so it is also a2/2/-11/2. Since a1/2/b1/2=(a/b)1/2, we can write this as (a2/-1)1/2, which is also equal to -a2/2. -a2/2 =a2/2i, or just ai. What do you guys think?

i have lot of doubts regarding polynomials and numerical method .. can someone help me understand some basics of it ... ? how do i dissassemble this sofa of polynomial properly ? and how does numerical method help ? can i have an example of a simple problem where i can utilize numerical method ???

Is there a web site giving out a lot of difficult questions about the additional mathematics or just mathematics? I appreciate who helps me very much. I want to have far more troublesome questions:P

I discovered a Law for Prime Numbers. I have for the couple of years searched ways of finding a law which will determine the prime numbers. As we all know, the law which will allow us to predict prime numbers are unknown. Unfortunately, today, I cannot still offer any remarkable law which will determine prime numbers, but I did find another law for prime numbers along the way. The Law States: The sum of all numbers which make up a prime will give you a number which will never be allowed to be a multiple of 3, nor do any digits ever make the sum of 12 to allow 3 to be divided, with the only acception of the the second prime number that is 3. If after you have taken…

Imagine that you are given a smooth space of unknown geometry. What kind of constructions would you use to figure out the number of dimensions of this space?

Necromancy! I searched the forum for 'Möbius' and this thread was the only one returned. And wonder of wonders you have mentioned just the concept I had in mind, i.e. squashing. Before I launch into squashed space I would just point out that above you say 'at the ends' and a Möbius band has no ends. So a few years back I got to wondering if there was a limit of L to W beyond which I could not join W's to get a Möbius band. I made paper bands as well as sewed some of canvas. Anyway, yes Möbius bands beyond certain ratios must be squishified. At some ratios the band squishes into a hexagon. After seeing it [the hexagon] and having recently read about the mysterious hexa…

This article explains why the cardinality of a set must be either Aleph0 or |ℝ|. In "Cardinality of the set of binary-expressed real numbers" I have shown that binary numbers cannot fill the unit real interval in spite of infinity of digits. In general, the members of a discrete set can only occupy isolated points in a continuous space leaving empty intervals behind. So, the fundamental difference between a continuum and a discrete set is the continuity, not the number of elements. Continuity and discreteness are collectively exhaustive and mutually exclusive. The cardinality of discrete set is aleph0, that of cintinuous set is |ℝ|. Because a set must be continuous or d…

I've read that some believe that Phidias, whose name was given to the Golden Ratio Phi, was the first to use the ratio in his sculptures, others say it goes further back in history to the Summerians. It appears frequently in nature,but, what causes it's existence?

Cantor used the expression 2^aleph0 in order to represent the magnitude of R set. Since base 2 can be represented as a tree diagram, we can use it in order to research a collection of infinitely many elements. For example, let us look at the infinitely long Top_to_Bottom blue tree, which is also represented as {1, 2, 4, 8, 16, ...}. It is obvious that we always find finitely many leafs in any arbitrary level of this tree, so this tree cannot have the magnitude of 2^aleph0. Furthermore, since in any arbitrary level we are still in N set, we can never define aleph0 as a transfinite number. Now let us say that we start by a collection of infinitely man…

I am looking for a quick proof that [math] 0^0=1 [/math] some kind of argument, doesnt have to be fancy Thank you e.g. let x = 0^0 therefore ln x = 0 ln 0 It's provable from the field axioms that 0*y=0, for any number y. Hence ln x = 0 therefore x=1 QED I am looking for other proofs. PS: And i know that lim x-->0+ of x = -infinity [math] \lim_{x \to 0^+} ln x = - \infty [/math] That's why I want a different proof, because the above isn't one.

Why do we teach our kids that 6 ÷ 3 = 2? If I divide 6 oranges in 3, what I get is not 2 oranges, but 2+2+2, without subtracting 4 oranges. So why don't we teach 6 ÷ 3 = 2+2+2, 1÷2 = 0.5+0.5, etc etc? If I say "I would like a quarter of this cake", then I am not dividing, but I am dividing and subtracting, I am doing a fraction, 1/4. Don't you think divisions shouldn't be confused with fractions?

Hello again folks. Is the following of any interest if it can be proved? P: Relative to any finite set of primes there are infinitely many pairs of consecutive twin primes. Note 1. In case it's the wrong word - by 'relative' I mean that none of the primes in the set are factors of the pair of twin primes. Note 2. This is nothing like a proof of the TPC. Thanks for any replies.

Two identical ships next to each other in the middle of a river heading against the current; one at full throttle developing 1000 horsepower just counteracts the current and does not advance at all. The other is anchored. How many horsepower does the anchor produce ?

i can't quite work this one out... i think the first step is to say that we want to find complex root of this: z^{n} = a but yeah...i dunno...can someone give me a few pointers please Sarah

Hi everyone! Lately at school we've been dealing with logarithmic inequations and they seem pretty tricky. So I was wondering if anyone could add a link or just post some useful hints that would help solving these inequations. I'd appreciate any kind of help!

Dont tell me the answer but how easy is this to do? X = 3 √(X+3)3 - (X+1)3 + (X+8) 3 find X...

Just a general question, may be practical or philosophical, what is your motivation for studying mathematics? My motivation is that I believe that a deeper understanding of nature can only be archived by understanding (and generalising) the mathematical structures found in theoretical physics. Much like category theory studies via abstraction the "mathematics of mathematics", mathematical physics deals with the mathematical structures found in theoretical physics without direct reference to the original physical systems. The generic idea is that we learn more about nature by abstraction. This I believe will become more and more true as time goes on and the too…