Hi everybody,
I have a question concerning a "stupid" thing i did today. I found a electric multimeter (if it is called so- you know, the device that measures dc current, the resistance in Ohms, dc and rms of ac voltage...), and thought to measure my body resistance. I didn't even think that...
Hi everybody,
I have just started reading some things about generalised functions, and i have some question. The source I am reading from is a book of partial differential equations so it's not a very formal introduction to generalized functions and functionals, but there are some basic...
Hi everybody,
I have a question concerning limits of 2-variable real functions and complex functions of 1 complex variable. When we have a function f:A->R, (A<=RxR and (0,0)εΑ) and we are looking if the limit of f at (0,0) exists, then we can do a substitution to polar co-ordinates like...
Hi everybody,
I have one question about integrals. I know the definition of an indefinite or definite integral but I am not sure I understand the notation. The indefinite integral of a function f:R->R (assuming that it exists) is noted like this \int f(x)dx Is the notation f(x)dx a...
Hi everybody,
I would like to know your opinion about this:
The (-) minus sign is used to represent both negative numbers and subtraction. Of course, subtraction is a special case of addition, but we definitely use this operation instead of always writing a+(-b) for example. So my...
Hi everybody,
This may have been discussed before ( and by me) but I would like to see a proof of the following statement:
" (ab)+(ac)=ab+ac"
Ok let me explain a bit. When we want to set some axioms about the real numbers we say that we define two functions from RxR->R, addition(+) and...
Hi everybody,
I was wondering if anyone can suggest any really interesting math problem, as I seem to have reached a point where I am tired of reading theory and need to focus on some serious problem. I have studied Calculus 1 and 2(=single and multivariable calculus for Real numbers) ,some...
Hi everybody,
My question is: how do we prove that the ratio of a circle's circumference to its diameter is a certain real number, the same for any circle (which we call pi)? If the proof is difficult to post, could you suggest some books that may include it because i haven't found one yet...
Hi everybody,
I have one question about vectors of R^3:
First of all, a point is described by its co-ordinates (x,y,z).
A vector r is described in this way: r=ax+by+cz ,where {x,y,z} is the standard basis (the numbers a,b,c are the "coordinates" of the vector). But i have seen in several...
Question for the "old" members of the forum
Hi everybody,
This is a question mostly for the older members of the forums or anynone who knows. I was wondering if any important mathematical result has been firstly posted here, or if there is anything interesting that has come up through the...
Hi everybody,
I need your help in one easy-looking problem that has confused me a bit.
Suppose we have a small cyclic object of mass m, just like in the picture, on a smooth surface. A steady force F is pulling it. The force is always on point A, like in the picture. Describe the object's...
Hi everybody,
I have recently read some things about what consistency of a system of axioms is and it really seems an important matter to me. So I would like to ask 2 things:
1)Have we proved the conistency of the real number algebra? I have read that some of the axioms of ZF-Set Theory...
Hi everybody,
I am searching for a Calculus book that is focused on exercises and not on theory. I am studying multivariable functions and I need a book with lots of solved exercises. I especially want to focus on the double,triple,surface and line integrals. Any suggestions??
Thanks
"Principia Mathematica" worth "reading"?
Hi everybody,
I have read about Principia Mathematica in many books, and sites on the Net, so I would like to ask you if you know anything about it,or even read some parts of it. What is it exactly ? Is this really important? I read that Godel has...
Hi everybody,
I have a question about the proof that the area of a square is a^2. I have read that we use these axioms do define area:
1) Equal polygon surfaces have the same(equal) area.
2)if we divide a polygon surface in a finite number of separate surfaces then the total area is equal...
Hi everybody,
You have propably found this test while searching the net but I am curious to see if anyone of you can solve any of its questions.Here's the link to it and to some others ,much easier. It's the one for exceptional intelligence...
Hi everybody,
When we have two sets A and B , we define the cartesian product of A and B as the set A*B={(x,y): (x element of A) and (y element of B)}. We also define A*A*...*A (n factors)=A^n. So when we write (A^2)*B, this is the same as A*A*B? I mean, for example (R^2)*R is the same as...
"Construction" of "number system"
Hi everybody,
How is the number system created and defined? I am talking about the natural numbers, but I am not actually asking about the definition and properties of N (Peano) but for the way that we have agreed to produce numbers. I mean, we have defined...
Hi everybody,
Mathematical theories are always based on some axioms. What else makes up an axiomatic theory? I mean , except from the axioms, we need some logical rules to draw conclusions and some definitions. What exactly are these definitions? (define definition!) I mean, can we use these...
Hi everybody,
This must have been discussed before but I would like to hear your opinions about the above question. Are mathematics just an invention, a creation of humans that helps them in their everyday life, or are they actually connected to nature, and are part of it that we just...
Hi everybody,
I would like to hear your comments about "The World of Mathematics Vol3" by James Newman. It has many essays of famous mathematicians and much stuff is about mathematical logic,mathematical way of thinking etc. Have you found it helpful in these topics?
Thanks
Hi everybody,
I didn't know where to post this, but it seems to me here is quite a good place. I would like to share some of my thoughts-questions about mathematical thinking and i would like to here your opinions.
Is it "normal" for somebody familiar with mathematics and really...
Hi everybody,
I would like to ask two things:
1)What is the line of real numbers? Is it just a graphical way of representing the set of real numbers?
2)How is the existence of transcendental numbers explained? I mean, if we look at the number line, and thinking of the Dedekind cuts...
Hi everybody,
How do we define positive and negative numbers? Also, how do we prove that (-a)(-b)=ab and also that if a<b then ac<bc for c>0 and ac>bc for c<0 ?
Thanks
Hi everybody,
I guess most of you know how a function is defined from a set A to a set B. How do we prove that many different functions exist (usually, if sets A and B are for example R) from A to B? Of course we can come up with many different functions, real ones for example, but is there...
Hi everybody,
We define multiplication as an operation with these properties :
a(b+c)=ab+ac and (a+b)c=ac+bc ,a*0=0 and a*1=a with a,b,c natural numbers and of course the two properties Zurtex mentioned ab=ba and a(bc)=(ab)c-I "forgot" to mention them because I didn't use them in what is...
Hi everybody,
I would like to find proofs for the algorithms that we use to calculate sums,products,quotients... For example I would like to see how the long division algorithm is proved. Do you know any sites that have such proofs? Any help would be appreciated
Thanks
I am wondering if it is worth spending much of your time=>much of your life, in order to study mathematics. Why do we give mathematics so much importance? Of course, they are really convienient and make many things easier in our lives , but I don't think that mathematicians actually find this...
Hi everybody,
I am looking for books about Logic and Set Theory. In particular, I am looking for not very advanced books. What are axioms, how do theorems connect to the axioms, how are we sure that some methods of proving give always correct and general results-these are some of the questions...